3. Compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let 2 2 3 4 A = -1 B = 0 1 1 2 1 -5 6 -- 2² C = -- --8 [9] D = E = 1 2 2 (a) A - 2B (b) 5E - C (c) DB -3 (d) EC
3. Compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let 2 2 3 4 A = -1 B = 0 1 1 2 1 -5 6 -- 2² C = -- --8 [9] D = E = 1 2 2 (a) A - 2B (b) 5E - C (c) DB -3 (d) EC
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 Operations
#### Problem Statement
Compute each matrix sum or product if it is defined. If an expression is undefined, explain why.
Given matrices:
\[ A = \begin{bmatrix} 1 & 2 & -3 \\ 0 & 1 & 1 \end{bmatrix} \]
\[ B = \begin{bmatrix} 2 & 3 & 1 \\ 1 & 2 & -3 \end{bmatrix} \]
\[ C = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \]
\[ D = \begin{bmatrix} -5 & 6 \\ 2 & -1 \end{bmatrix} \]
\[ E = \begin{bmatrix} 3 \\ 0 \end{bmatrix} \]
### Questions
(a) \( A - 2B \)
(b) \( 5E - C \)
(c) \( DB \)
(d) \( EC \)
### Detailed Explanation:
**(a) A - 2B**:
- **Matrix A** is a 2x3 matrix.
- **Matrix B** is a 2x3 matrix as well.
- First, compute \(2B\) (scalar multiplication of matrix B by 2):
\[ 2B = \begin{bmatrix} 4 & 6 & 2 \\ 2 & 4 & -6 \end{bmatrix} \]
- Then, subtract 2B from A:
\[ A - 2B = \begin{bmatrix} 1 & 2 & -3 \\ 0 & 1 & 1 \end{bmatrix} - \begin{bmatrix} 4 & 6 & 2 \\ 2 & 4 & -6 \end{bmatrix} = \begin{bmatrix} 1-4 & 2-6 & -3-2 \\ 0-2 & 1-4 & 1+6 \end{bmatrix} = \begin{bmatrix} -3 & -4 & -5 \\ -2 & -3 & 7 \end{bmatrix} \]
**(b) 5E - C**:
- **Matrix E** is a 2x1 vector.
- **Matrix C** is a 2x2 matrix.
- Compute \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d07e113-70c7-44ea-a54a-4dad627b44c8%2F465b06ef-b215-4dd7-a061-2997ab8e083b%2F7r5m4rl_processed.png&w=3840&q=75)
Transcribed Image Text:### Matrix Operations
#### Problem Statement
Compute each matrix sum or product if it is defined. If an expression is undefined, explain why.
Given matrices:
\[ A = \begin{bmatrix} 1 & 2 & -3 \\ 0 & 1 & 1 \end{bmatrix} \]
\[ B = \begin{bmatrix} 2 & 3 & 1 \\ 1 & 2 & -3 \end{bmatrix} \]
\[ C = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \]
\[ D = \begin{bmatrix} -5 & 6 \\ 2 & -1 \end{bmatrix} \]
\[ E = \begin{bmatrix} 3 \\ 0 \end{bmatrix} \]
### Questions
(a) \( A - 2B \)
(b) \( 5E - C \)
(c) \( DB \)
(d) \( EC \)
### Detailed Explanation:
**(a) A - 2B**:
- **Matrix A** is a 2x3 matrix.
- **Matrix B** is a 2x3 matrix as well.
- First, compute \(2B\) (scalar multiplication of matrix B by 2):
\[ 2B = \begin{bmatrix} 4 & 6 & 2 \\ 2 & 4 & -6 \end{bmatrix} \]
- Then, subtract 2B from A:
\[ A - 2B = \begin{bmatrix} 1 & 2 & -3 \\ 0 & 1 & 1 \end{bmatrix} - \begin{bmatrix} 4 & 6 & 2 \\ 2 & 4 & -6 \end{bmatrix} = \begin{bmatrix} 1-4 & 2-6 & -3-2 \\ 0-2 & 1-4 & 1+6 \end{bmatrix} = \begin{bmatrix} -3 & -4 & -5 \\ -2 & -3 & 7 \end{bmatrix} \]
**(b) 5E - C**:
- **Matrix E** is a 2x1 vector.
- **Matrix C** is a 2x2 matrix.
- Compute \(
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