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Perform the matrix operation. Let A = [22] -8-8 O 4 -3] -16-4 0-3 (0-12] -3 0-12 and B = Find A - B.

Perform the matrix operation. Let A = [22] -8-8 O 4 -3] -16-4 0-3 (0-12] -3 0-12 and B = Find 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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Linear algebra
**Matrix Subtraction Problem** **Task:** Perform the matrix operation. **Given:** Matrix \( A = \begin{bmatrix} -2 & 2 \\ -8 & -8 \end{bmatrix} \) Matrix \( B = \begin{bmatrix} 2 & 5 \\ -8 & 4 \end{bmatrix} \) **Find:** \( A - B \) **Options:** 1. \( \begin{bmatrix} 4 & -3 \\ -16 & -4 \end{bmatrix} \) 2. \( \begin{bmatrix} 0 & -3 \\ 0 & -12 \end{bmatrix} \) 3. \( \begin{bmatrix} -4 & -3 \\ 0 & -12 \end{bmatrix} \) 4. \( \begin{bmatrix} 0 & 3 \\ -16 & 12 \end{bmatrix} \) **Explanation of Matrix Subtraction:** Matrix subtraction involves subtracting corresponding elements of two matrices. For matrices \( A \) and \( B \), each element in \( A - B \) is computed as follows: - Subtract the element in the first row, first column of \( B \) from the element in the first row, first column of \( A \): \((-2) - 2 = -4\). - Subtract the element in the first row, second column of \( B \) from the element in the first row, second column of \( A \): \(2 - 5 = -3\). - Subtract the element in the second row, first column of \( B \) from the element in the second row, first column of \( A \): \((-8) - (-8) = 0\). - Subtract the element in the second row, second column of \( B \) from the element in the second row, second column of \( A \): \((-8) - 4 = -12\). **Result:** The correct matrix \( A - B = \begin{bmatrix} -4 & -3 \\ 0 & -12 \end{bmatrix} \), which corresponds to option 3.
Transcribed Image Text:**Matrix Subtraction Problem** **Task:** Perform the matrix operation. **Given:** Matrix \( A = \begin{bmatrix} -2 & 2 \\ -8 & -8 \end{bmatrix} \) Matrix \( B = \begin{bmatrix} 2 & 5 \\ -8 & 4 \end{bmatrix} \) **Find:** \( A - B \) **Options:** 1. \( \begin{bmatrix} 4 & -3 \\ -16 & -4 \end{bmatrix} \) 2. \( \begin{bmatrix} 0 & -3 \\ 0 & -12 \end{bmatrix} \) 3. \( \begin{bmatrix} -4 & -3 \\ 0 & -12 \end{bmatrix} \) 4. \( \begin{bmatrix} 0 & 3 \\ -16 & 12 \end{bmatrix} \) **Explanation of Matrix Subtraction:** Matrix subtraction involves subtracting corresponding elements of two matrices. For matrices \( A \) and \( B \), each element in \( A - B \) is computed as follows: - Subtract the element in the first row, first column of \( B \) from the element in the first row, first column of \( A \): \((-2) - 2 = -4\). - Subtract the element in the first row, second column of \( B \) from the element in the first row, second column of \( A \): \(2 - 5 = -3\). - Subtract the element in the second row, first column of \( B \) from the element in the second row, first column of \( A \): \((-8) - (-8) = 0\). - Subtract the element in the second row, second column of \( B \) from the element in the second row, second column of \( A \): \((-8) - 4 = -12\). **Result:** The correct matrix \( A - B = \begin{bmatrix} -4 & -3 \\ 0 & -12 \end{bmatrix} \), which corresponds to option 3.
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