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9. Let A, B be the same matrices from problem 8. If AB - BA = -BA-athen c O c = 8,d=-4 Oc=9, d= -2 Oc=9, d=-3 Oc=8, d=-1

9. Let A, B be the same matrices from problem 8. If AB - BA = -BA-athen c O c = 8,d=-4 Oc=9, d= -2 Oc=9, d=-3 Oc=8, d=-1

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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**Matrix Commutation Problem** **Problem 9:** Let \( A \), \( B \) be the same matrices from problem 8. If \( AB - BA = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \), then determine the values of \( c \) and \( d \). **Options:** - \( \circ \) \( c = 8 \), \( d = -4 \) - \( \circ \) \( c = 9 \), \( d = -2 \) - \( \circ \) \( c = 9 \), \( d = -3 \) - \( \circ \) \( c = 8 \), \( d = -1 \) **Explanation:** This problem involves finding the specific values for \( c \) and \( d \) in the resulting matrix after subtracting the product of matrix \( B \) and matrix \( A \) from the product of matrix \( A \) and matrix \( B \). The solution involves evaluating \( AB - BA \) and comparing it to the matrix \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\). **Note:** This problem assumes prior knowledge of matrix multiplication and properties.
Transcribed Image Text:**Matrix Commutation Problem** **Problem 9:** Let \( A \), \( B \) be the same matrices from problem 8. If \( AB - BA = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \), then determine the values of \( c \) and \( d \). **Options:** - \( \circ \) \( c = 8 \), \( d = -4 \) - \( \circ \) \( c = 9 \), \( d = -2 \) - \( \circ \) \( c = 9 \), \( d = -3 \) - \( \circ \) \( c = 8 \), \( d = -1 \) **Explanation:** This problem involves finding the specific values for \( c \) and \( d \) in the resulting matrix after subtracting the product of matrix \( B \) and matrix \( A \) from the product of matrix \( A \) and matrix \( B \). The solution involves evaluating \( AB - BA \) and comparing it to the matrix \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\). **Note:** This problem assumes prior knowledge of matrix multiplication and properties.
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