Explanation Given: The matrix A is [ 1 1 0 1 0 1 6 2 3 ] and the matrix B is [ − 2 − 3 1 3 3 11 2 4 − 1 ] . Approach: If A = [ a ij ] is m × n matrix, and B = [ b ij ] is n × p matrix, then the product A B is m × p matrix given by, A B = [ c ij ] Here, c i j = a i 1 b 1 j + a i 2 b 2 j + a i 3 b 3 j + ... + a i n b n j ... ( 1 ) If an n × n A − 1 such that A B − 1 = I n = B − 1 A , then B − 1 is called the inverse of A . Calculation: From the above condition, The number of rows in matrix A is 2 and the number of column in the matrix is 2 . Similarly the number of rows in matrix B is 2 and the number of column in the matrix is 2 . Since the number of column of the matrix A is equal to the number of row of the matrix B , so, the product of the above matrix is possible. From equation ( 1 ) , the value of A B is given as, A B = [ 1 1 0 1 0 1 6 2 3 ] [ − 2 − 3 1 3 3 − 1 2 4 − 1 ] = [ 1 ( − 2 ) + 1 ( 3 ) + 0 ( 2 ) 1 ( − 3 ) + 1 ( 3 ) + 0 ( 4 ) 1 ( 1 ) + 1 ( − ) + 0 ( − 1 ) 1 ( − 2 ) + 0 ( 3 ) + 1 ( 2 ) 1 ( − 3 ) + 0 ( 3 ) + 1 ( 4 ) 1 ( 1 ) + 0 ( − 1 ) + 1 ( − 1 ) 6 ( − 2 ) + 2 ( 3 ) + 3 ( 2 ) 6 ( − 3 ) + 2 ( 3 ) + 3 ( 4 ) 6 ( 1 ) + 2 ( − 1 ) + 3 (

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ISBN: 9781337271073

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 8.CR, Problem 67CR

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The matrix B=[−2−31331124−1] is inverse of A=[110101623].

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Chapter 8.CR, Problem 66CR

Chapter 8.CR, Problem 68CR

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The matrix B = [ − 2 − 3 1 3 3 11 2 4 − 1 ] is inverse of A = [ 1 1 0 1 0 1 6 2 3 ] .

Solution Summary: The author explains that the matrix A is mtimes n matrix, and B inverses it.

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To show:

The matrix B=[−2−31331124−1] is inverse of A=[110101623].

Want to see the full answer?

Chapter 8 Solutions

The matrix B = [ − 2 − 3 1 3 3 11 2 4 − 1 ] is inverse of A = [ 1 1 0 1 0 1 6 2 3 ] .

Solution Summary: The author explains that the matrix A is mtimes n matrix, and B inverses it.

Videos

To show: The matrix B=[−2−31331124−1] is inverse of A=[110101623].

Want to see the full answer?

Chapter 8 Solutions

To show:

The matrix B=[−2−31331124−1] is inverse of A=[110101623].