A Survey of Mathematics with Applications (11th Edition)
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Binary ; Addition, subtraction, division, and ... more
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Single ; When a binary operation is performed on ... more
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Closed ; If a binary operation is performed on two... more
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Counterexample ; Counterexample is an example that... more
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Identity ; When anadditive element is added with ... more
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Multiplicative ; When anelement is multiplied with... more
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Inverse ; Consider two numbers and.Add the ... more
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Group ; The mathematical system that satisfies the... more
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Commutative ; The result of a binary operation on ... more
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Abelian ; The result of a binary operation on two ... more
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For two elements, the addition commutative ... more
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For two elements of the set, the multiplication ... more
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For three elements of the set, multiplication ... more
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For three elements of the set, addition ... more
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; The result of binary operation on two elements ... more
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; The result of binary operation on two elements ... more
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; Associative property of division states that if... more
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; Associative property of subtraction states that... more
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Yes, all the four properties to form a group which... more
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Yes, all the five condition to form a group which ... more
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No, the closure property is not satisfied which ... more
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No, the closure property is not satisfied which ... more
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Yes, all the five condition to form a group which ... more
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No ; The whole numbers include the numbers shown ... more
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No ; The negative integers include the numbers ... more
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No ; Integers include the numbers shown in the set... more
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No ; Rational numbers include the numbers that are... more
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No ; Rational numbers include the numbers that are... more
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No ; Irrational numbers are the set of real number... more
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No ; Irrational numbers are the set of real number... more
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The set of rational numbers is a group under ... more
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; The set of clock 12 arithmetic with elements of... more
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Closed ; If the binary operation performed on two ... more
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Identity ; Identity element is a special type of ... more
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Inverse ; 12 is the additive identity of clock 12 ... more
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Associative ; In the mathematical system, if the ... more
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Commutative ; If the result of binary operation of... more
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Commutative ; If a group with binary operation ... more
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Associative ; If every element does not appear in ... more
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Commutative ; The result of binary operation of 2 ... more
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Non-abelian ; A group with binary operation is ... more
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3 ; The sum follows commutative property.Refer to ... more
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6 ; The sum follows commutative property.Refer to ... more
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4 ; The sum follows commutative property.Refer to ... more
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12 ; The sum follows commutative property.Refer to... more
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8 ; Refer to the table and find the value placed ... more
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9 ; Refer to the table and find the value placed ... more
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; Let the time be 4 o'clock. To find the time 10 ... more
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; Let the time be 1 o'clock. To find the time 12 ... more
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; Let the time be 6 o'clock. To find the time 10 ... more
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; Let the time be 5 o'clock. To find the time 8 ... more
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; Let the time be 5 o'clock. To find the time 5 ... more
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; Let the time be 12 o'clock. To find the time 12... more
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123456123456123456123456123456123456123456123456... more
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; Let the time be 4 o'clock. To find the time ... more
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; Let the time be 5 o'clock. To find the time 2 ... more
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; Let the time be 4 o'clock. To find the time 5 ... more
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; Let the time be 3 o'clock. To find the time 5 ... more
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; Let the time be 1 o'clock. To find the time 3 ... more
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... more
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6 ; Let the time be 6 o'clock. To find the time ... more
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3 ; Generate the table of clock 7 arithmetic under... more
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6 ; Generate a table of clock 7 arithmetic under ... more
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7 ; Generate a table of clock 7 arithmetic under ... more
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7 ; Generate a table of clock 7 arithmetic under ... more
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The clock 7 arithmetic system is a commutative ... more
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Closure propertyAssociative property ; Check the ... more
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Associative propertyCommutative property ; Let the... more
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InverseAssociative property ; Check the five ... more
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Commutative propertyAssociative property ; Let the... more
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Inverse of 0, 2, 3, and 5 does not exist. ; Let ... more
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In the practice of medicine, the 24-hour clock is ... more
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; For instance, the set of elements in a modulo 5... more
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binary ; A binary operation is an operation that ... more
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remainder ; Modulus classes are the set of ... more
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modulus ; In a modulo system, a solution, if ... more
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congruent ; By the definition of congruent, if two... more
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divide ; By the definition of congruent, if any ... more
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Day F ; Assume the number of days in a week as a ... more
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Day SU ; Divide 1095 by 7 to find the remainder., ... more
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Day F ; Divide 400 by 7 to find the remainder., ... more
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Month AU ; Divide to find the remainder., ... more
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Month JU ; Divide by 12 to find the remainder., ... more
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Month S ; Divide 83 by 12 to find the remainder., ... more
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Month O ; Divide by 12 to find the remainder., ... more
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Month JUL ; Assume 12 month as a modulo 12 ... more
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Month JUL ; Assume the given system as a modulo 12... more
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; The difference of the given numbers is .7 does ... more
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; The product of the given numbers is .72 does ... more
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; The product of the given numbers is .56 does ... more
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; Add 5 or any multiple of 5 in modulo 5.Their ... more
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; Add 5 or any multiple of 5 in modulo 5.Their ... more
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; Perform the indicated operate in the ... more
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; The difference is , and the product of the ... more
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1 ; Divide 43 by 6 to determine the number that is... more
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5 ; Divide 41 by 9 to determine the number that is... more
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5 ; Divide 75 by 8 to determine the number that is... more
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; Add 7 or a multiple of 7 to a number in modulo ... more
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; Add 4 or a multiple of 4 to a number in modulo ... more
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; Add 8 or a multiple of 8 to a number in modulo ... more
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; Add 7 or any multiple of 7 in modulo 7.Their ... more
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4 ; Adding 4 to 5 yields 9 and 9 is congruent to 3... more
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4 ; Adding 4 to 3 yields 7 and 7 is congruent to 2... more
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3 ; Adding 3 to 6 yields 9 and 9 is congruent to 2... more
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5 ; Adding 5 to 4 gives 9 and 9 is congruent to 3 ... more
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5 ; In modulo 6, adding 6 or a multiple of 6 to a ... more
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5 ; In modulo 9, adding 9 or a multiple of 9 to a ... more
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5 ; To determine the solution, replace the ... more
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6 ; To determine the solution, replace the ... more
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No solution ; Replace the question mark with the ... more
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No solution ; Replace the question mark with the ... more
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; Replace the question mark with the numbers 0, 1... more
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; Replace the question mark with the numbers 0, 1... more
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5 ; Add 12 to the given problem so that the given ... more
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7 ; Add 12 to the left side of the given problem ... more
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2 ; Use the property , which means .The digit 12 ... more
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; Use the property, whichmeans. Divide 24 by 7 ... more
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; Assume (mod m).Replace the question mark with ... more
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; Use the relation (mod m), which means(mod m), ... more
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0 ; Replace with number 1.Determine the ... more
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1 ; Replace with number 1.Determine the ... more
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2 ; Replace with number 1.Determine the ... more
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; Write the congruent relation by using the given... more
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KNOWLEDGE IS POWER ; Use the coding circle to find... more
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; Determine the number of rotations of wheel in a... more
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The Enigma machine was used to encode and decode ... more
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Gauss created the method of congruences, its ... more
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Matrix ; A matrix is defined as a collection of ... more
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Square matrix ; Every matrix consists of rows and ... more
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; The notation is used to express the dimension ... more
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; The notation is used to express the dimension ... more
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Dimensions ; Two or more matrices can only be ... more
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Scalar ; The product of a matrix and a real number... more
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Columns ; To multiply two matrices, it is ... more
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Group ; There are five properties of matrix ... more
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; Substitute for and for into the expression ... more
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; Substitute for and for into the expression ... more
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; Substitute for and for into . ; more
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; Substitute for and for into . ; more
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; Multiply each entry of matrix by 2. ; Multiply... more
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; Multiply each entry of matrix by 3. ; Multiply... more
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; Substitute as and as into to find the ... more
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; Substitute as and as into to find the ... more
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; Substitute as and as into to find the ... more
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; Substitute as and as into to find the ... more
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; The given matrices and have the same ... more
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; The given matrices, and, have the same ... more
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;Multiplication cannot be performed as the number ... more
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;Multiplication cannot be performed as the number ... more
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Addition cannot be performed as the dimensions of ... more
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Addition cannot be performed as the dimensions of ... more
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Addition cannot be performed as the dimensions of ... more
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Addition cannot be performed as the dimensions of ... more
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Entire Proof Answer: Substitute for and for ... more
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Entire Proof Answer: Substitute for and for ... more
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Entire Proof Answer: Substitute for and for ... more
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Entire Proof Answer: Substitute for , for , and... more
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Entire Proof Answer: Substitute for, for, and ... more
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Entire Proof Answer: Substitute for , for , and... more
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Entire Proof Answer: Substitute for , for , and... more
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No ; Substitute for and for into. ; Substitute... more
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Yes ; Substitute for and for into . ; ... more
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Yes ; Substitute for and for into . ; ... more
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Entire Proof Answer: Substitute as , as, and as... more
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Entire Proof Answer: Substitute as , as, and as... more
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Entire Proof Answer: Substitute as, as , and as... more
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Entire Proof Answer: Substitute as, as, and as ... more
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; Add the given matrices and .The first column ... more
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; Subtract the given matrix from matrix . The ... more
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; Multiply the given matrix with matrix to find... more
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; Assume to be the matrix showing a typical day’... more
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; Substitute for and for and perform matrix ... more
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Entire Proof Answer: Let and be two matrices ... more
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Entire Proof Answer: Assume, , and to be the ... more
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Yes ; Assume and to be two matrices, and , ... more
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Entire Proof Answer: Assume , , and to be three ... more
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Entire Proof Answer: Substitute for and for ... more
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The multiplication of the inverse of coefficient ... more
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Assume a scenario where a Person K runs three ... more
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The method of protecting information and ... more
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A binary operation is the mathematical calculation... more
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Set of elementsBinary operation ; There are 2 ... more
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No, as the division of two whole numbers is not ... more
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Yes, as the difference of any two real numbers is ... more
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9 ; Generate the table of clock 12 arithmetic ... more
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Closure: If the binary operation result the ... more
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Yes, as a set of integers satisfies all the four ... more
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A set of integers under a multiplication does not ... more
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No; the absence of identity element and inverse ... more
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No, the absence of inverse element implies they do... more
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Identity element and inverse element ; The ... more
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Inverse element propertyAssociative property ; The... more
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Associative Property ; The mathematical system can... more
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; In Modulo System, the solution will be in the ... more
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; In Modulo System, the solution will be in the ... more
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; In Modulo System, the solution will be in the ... more
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; The sum is equal to 7, which are not in the set... more
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; Add 7 to the given problem so that the given ... more
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3 ; Replace the question mark with the numbers 0, ... more
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; Replace the question mark with the numbers 0, 1... more
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4 ; The product is equal to 70, which are not in ... more
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9 ; Replace the question mark with the numbers 0, ... more
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No solution. ; Replace the question mark with the ... more
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; Replace the question mark with the numbers 0, 1... more
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+012345001234511234502234501334501244501235501234... more
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012300000101232020230321Not Commutative group. ; ... more
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; Both the matrices have 2 rows and 2 columns, ... more
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; Both the matrices have 2 rows and 2 columns, so... more
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; Calculate the value of the matrix by ... more
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; Matrix contains 2 columns and matrix contains... more
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; Matrix contains 2 columns and matrix contains ... more
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A system that consists of a set of elements with ... more
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ClosureAssociativityIdentity elementInverse ... more
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Yes, the set of integers satisfies all the 4 ... more
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No, the set of integers are not commutative, ... more
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+12345123451234512345123451234512345 ; Draw clock ... more
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Yes ; A set of integers consists of 0, positive ... more
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The mathematical system is not a commutative group... more
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The mathematical system is a commutative group. ; ... more
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The mathematical system is a commutative group. ; ... more
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4 ; As the working modulo is modulo 6, replace the... more
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; It is known that as .Determine the positive ... more
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; Add 9 to the number 3 as it will not change ... more
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No solution ; As the working modulo is modulo 6, ... more
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