Explanation Assuming the matrix, A = [ 2 1 3 1 ] , B = [ 4 7 1 2 ] Now, we will simplify the expression [ A + B ] − 1 = A − 1 + B − 1 as below, A = [ 2 1 3 1 ] , B = [ 4 7 1 2 ] For the expression, [ A + B ] = [ 2 1 3 1 ] + [ 4 7 1 2 ] = [ 2 + 4 1 + 7 3 + 1 1 + 2 ] = [ 6 8 4 3 ] Now, The inverse of matrix [ A + B ] is equal to: [ A + B ] − 1 = 1 a d − b c [ d − b − c a ] Now, compare the matrix to the original matrix. So, a = 6 b = 8 c = 4 d = 3 Now, the inverse is: [ A + B ] − 1 = 1 a d − b c [ d − b − c a ] Substitutes the values to get, [ A + B ] − 1 = 1 a d − b c [ d − b − c a ] = 1 − 6 [ 3 − 8 − 4 6 ] = [ − 1 2 4 3 2 3 − 1 ] Therefore, the inverse of the matrix [ A + B ] is [ − 1 2 4 3 2 3 − 1 ] invertible matrix

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ISBN: 9780134469140

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8.4, Problem 87PE

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Whether the statement “[A+B]−1=[A−1+B−1], assuming A,B and A+B is invertible” is true or false.

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Chapter 8.4, Problem 86PE

Chapter 8.4, Problem 88PE

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Ch. 8.1 - Check Point 1 Write the augmented matrix for the...Ch. 8.1 - Check Point 2 Use the matrix ...Ch. 8.1 - Check Point 3 Use matrices to solve the system:...Ch. 8.1 - Check Point 4 Use matrices to solve the system:...Ch. 8.1 - Check Point 5 Solve the system in Check Point. 3...Ch. 8.1 - Prob. 1CVC Ch. 8.1 - Fill in each blank so that the resulting statement...Ch. 8.1 - Prob. 3CVC Ch. 8.1 - Prob. 4CVC Ch. 8.1 - Fill in each blank so that the resulting statement...

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Whether the statement “ [ A + B ] − 1 = [ A − 1 + B − 1 ] , assuming A , B and A + B is invertible” is true or false.

Solution Summary: The author analyzes whether the statement " left[A+Bright]-1= left[A1+B] is invertible" is true or false.

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Whether the statement “[A+B]−1=[A−1+B−1], assuming A,B and A+B is invertible” is true or false.

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