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1. Given the following matrices: C = 7 -5 오 Compute each of the following, if possible. If not possible, explain why not. a. B+C b. C +D c. 2(B-3D) B= 4 -3 0 1 y D= 0 -3 5y

1. Given the following matrices: C = 7 -5 오 Compute each of the following, if possible. If not possible, explain why not. a. B+C b. C +D c. 2(B-3D) B= 4 -3 0 1 y D= 0 -3 5y

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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## Matrix Operations Exercise **Directions:** Show all work in a neat and organized manner and use equal signs appropriately. Clearly indicate your answers. 1. **Given the following matrices:** \( B = \begin{bmatrix} x & 0 & -6 \\ 4 & -3 & 0 \end{bmatrix} \) \( C = \begin{bmatrix} 2 & 3 \\ 7 & -5 \\ 1 & y \end{bmatrix} \) \( D = \begin{bmatrix} 8x & 2 & 1 \\ 0 & -3 & 5y \end{bmatrix} \) **Compute each of the following, if possible. If not possible, explain why not.** a. \( B + C \) b. \( C^T + D \) c. \( 2(B - 3D) \) --- ### Explanation: - **\( B + C \):** Check if matrix addition is possible by comparing the dimensions of \( B \) and \( C \). - **\( C^T + D \):** Transpose the matrix \( C \) and determine if the addition with \( D \) is possible by ensuring the dimensions match. - **\( 2(B - 3D) \):** Multiply matrix \( D \) by 3, subtract from \( B \), and then double the resulting matrix.
Transcribed Image Text:## Matrix Operations Exercise **Directions:** Show all work in a neat and organized manner and use equal signs appropriately. Clearly indicate your answers. 1. **Given the following matrices:** \( B = \begin{bmatrix} x & 0 & -6 \\ 4 & -3 & 0 \end{bmatrix} \) \( C = \begin{bmatrix} 2 & 3 \\ 7 & -5 \\ 1 & y \end{bmatrix} \) \( D = \begin{bmatrix} 8x & 2 & 1 \\ 0 & -3 & 5y \end{bmatrix} \) **Compute each of the following, if possible. If not possible, explain why not.** a. \( B + C \) b. \( C^T + D \) c. \( 2(B - 3D) \) --- ### Explanation: - **\( B + C \):** Check if matrix addition is possible by comparing the dimensions of \( B \) and \( C \). - **\( C^T + D \):** Transpose the matrix \( C \) and determine if the addition with \( D \) is possible by ensuring the dimensions match. - **\( 2(B - 3D) \):** Multiply matrix \( D \) by 3, subtract from \( B \), and then double the resulting matrix.
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