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2] Finding the Inverses of Products and Transposes In Exercises 41-44, use the inverse matrices to find (a) (AB)-1, (b) (A)-, and (c) (2A)-1. 41. A- = -7 7. B- = %3D 42. A = B

2] Finding the Inverses of Products and Transposes In Exercises 41-44, use the inverse matrices to find (a) (AB)-1, (b) (A)-, and (c) (2A)-1. 41. A- = -7 7. B- = %3D 42. A = B

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
#41
**Finding the Inverses of Products and Transposes** In Exercises 41-44, use the inverse matrices to find (a) \((AB)^{-1}\), (b) \((A^T)^{-1}\), and (c) \((2A)^{-1}\). 41. \( A^{-1} = \begin{bmatrix} 2 & 5 \\ -7 & 6 \end{bmatrix} \), \( B^{-1} = \begin{bmatrix} 7 & -3 \\ 2 & 0 \end{bmatrix} \) 42. \( A^{-1} = \begin{bmatrix} -\frac{2}{7} & \frac{1}{7} \\ \frac{3}{7} & \frac{2}{7} \end{bmatrix} \), \( B^{-1} = \begin{bmatrix} \frac{5}{11} & -\frac{2}{11} \\ \frac{3}{11} & -\frac{1}{11} \end{bmatrix} \)
Transcribed Image Text:**Finding the Inverses of Products and Transposes** In Exercises 41-44, use the inverse matrices to find (a) \((AB)^{-1}\), (b) \((A^T)^{-1}\), and (c) \((2A)^{-1}\). 41. \( A^{-1} = \begin{bmatrix} 2 & 5 \\ -7 & 6 \end{bmatrix} \), \( B^{-1} = \begin{bmatrix} 7 & -3 \\ 2 & 0 \end{bmatrix} \) 42. \( A^{-1} = \begin{bmatrix} -\frac{2}{7} & \frac{1}{7} \\ \frac{3}{7} & \frac{2}{7} \end{bmatrix} \), \( B^{-1} = \begin{bmatrix} \frac{5}{11} & -\frac{2}{11} \\ \frac{3}{11} & -\frac{1}{11} \end{bmatrix} \)
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