Explanation Approach: Let A be a n × n matrix and let I n be n × n identity matrix. If there exist a matrix A − 1 such that A A − 1 = I n And, A − 1 A = I n Then A − 1 is the inverse of A. Calculation: B is the inverse of A only if, A B = I … ( 1 ) And, B A = I ... ( 2 ) Simplify matrix B . B = 1 3 [ − 1 3 − 2 − 2 − 2 9 − 7 − 10 1 0 − 1 − 1 3 − 6 6 6 ] = [ − 1 / 3 1 − 2 / 3 − 2 / 3 − 2 / 3 3 − 7 / 3 − 10 / 3 1 / 3 0 − 1 / 3 − 1 / 3 1 − 2 2 2 ] Substitute [ − 1 / 3 1 − 2 / 3 − 2 / 3 − 2 / 3 3 − 7 / 3 − 10 / 3 1 / 3 0 − 1 / 3 − 1 / 3 1 − 2 2 2 ] for B , [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] for I and [ 2 0 2 1 3 0 0 1 − 1 1 − 2 1 3 − 1 1 0 ] for A in equation ( 1 ) . [ 2 0 2 1 3 0 0 1 − 1 1 − 2 1 3 − 1 1 0 ] [ − 1 / 3 1 − 2 / 3 − 2 / 3 − 2 / 3 3 − 7 / 3 − 10 / 3 1 / 3 0 − 1 / 3 − 1 / 3 1 − 2 2 2 ] = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] [ ( − 2 3 + 0 + 2 3 + 1 ) ( 2 + 0 + 0 − 2 ) ( − 4 3 + 0 − 2 3 + 2 ) ( − 4 3 + 0 − 2 3 + 2 ) ( − 1 + 0 + 0 + 1 ) ( 3 + 0 + 0 − 2 ) ( − 2 + 0 + 0 + 2 ) ( − 2 + 0 + 0 + 2 ) ( 1 3 − 2 3 − 2 3 + 1 ) ( − 1 + 3 + 0 − 2 ) ( 2 3 − 7 3 + 2 3 + 2 ) ( 2 3 − 10 3 + 2 3 − 2 ) ( − 1 + 2 3 + 1 3 + 0 ) ( 3 − 3 + 0 + 0 ) ( − 2 + 7 3 − 1 3 + 0 ) ( − 2 + 10 3 − 1 3 + 0 ) ] =

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Chapter 8.3, Problem 11E

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The matrix B=13[−13−2−2−29−7−1010−1−13−666] is the inverse of matrix A=[20213001−11−213−110].

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Chapter 8.3, Problem 10E

Chapter 8.3, Problem 12E

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Chapter 8 Solutions

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The matrix B = 1 3 [ − 1 3 − 2 − 2 − 2 9 − 7 − 10 1 0 − 1 − 1 3 − 6 6 6 ] is the inverse of matrix A = [ 2 0 2 1 3 0 0 1 − 1 1 − 2 1 3 − 1 1 0 ] .

Solution Summary: The author explains that the matrix B=13left is the inverse of matrix A.

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To show:

The matrix B=13[−13−2−2−29−7−1010−1−13−666] is the inverse of matrix A=[20213001−11−213−110].

Want to see the full answer?

Chapter 8 Solutions

The matrix B = 1 3 [ − 1 3 − 2 − 2 − 2 9 − 7 − 10 1 0 − 1 − 1 3 − 6 6 6 ] is the inverse of matrix A = [ 2 0 2 1 3 0 0 1 − 1 1 − 2 1 3 − 1 1 0 ] .

Solution Summary: The author explains that the matrix B=13left is the inverse of matrix A.

Videos

To show: The matrix B=13[−13−2−2−29−7−1010−1−13−666] is the inverse of matrix A=[20213001−11−213−110].

Want to see the full answer?

Chapter 8 Solutions

To show:

The matrix B=13[−13−2−2−29−7−1010−1−13−666] is the inverse of matrix A=[20213001−11−213−110].