Explanation Given Information: The provided matrix is [ a b c d ] and inverse is [ a b c d ] − 1 = 1 a d − b c [ d − b − c a ] where, a d − b c ≠ 0 . Consider the matrix [ a b c d ] . A matrix with m rows and n columns is of dimension m × n , where m and n are positive integers. Since, number of rows in [ a b c d ] is 2 and number of columns is 2 . Thus, dimension of [ a b c d ] is 2 × 2 . Since, number of rows in 1 a d − b c [ d − b − c a ] is 2 and number of columns is 2. Thus, dimension of 1 a d − b c [ d − b − c a ] is 2 × 2 . Now, two matrices A and B are inverse pairs if A B = I , where I is the n × n identity matrix. Since, number of columns in 1 a d − b c [ d − b − c a ] is equal to the number of rows in [ a b c d ] , the product ( 1 a d − b c [ d − b − c a ] ) [ a b c d ] is defined. For matrices A with dimension m × n and B with dimension n × k , the product AB is the matrix of dimension m × k and ij th entry of AB is the sum of product of corresponding entries of row i of A and column j of B . Since dimension of first matrix is 2 × 2 and dimension of second matrix is 2 × 2 , the dimension of the product is 2 × 2

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.3, Problem 71E

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Whether the inverse of matrix [abcd] is given by [abcd]−1=1ad−bc[d−b−ca] or not, where, ad−bc≠0 by the use of matrix multiplication.

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Chapter 5.3, Problem 70E

Chapter 5.3, Problem 72E

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Chapter 5 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

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Whether the inverse of matrix [ a b c d ] is given by [ a b c d ] − 1 = 1 a d − b c [ d − b − c a ] or not, where, a d − b c ≠ 0 by the use of matrix multiplication.

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Whether the inverse of matrix [abcd] is given by [abcd]−1=1ad−bc[d−b−ca] or not, where, ad−bc≠0 by the use of matrix multiplication.

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