Solve the matrix equation Ax = l for X, using the fact that A-! = X = Also solve the following matrix equation for Y. AY = Y =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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## Matrix Equation Solutions

### Problem 1: Solve for X

**Given Matrix Equation:**

\[ AX = \begin{bmatrix} 3 \\ 15 \end{bmatrix} \]

To solve for \( X \), use the inverse of matrix \( A \):

\[ A^{-1} = \begin{bmatrix} -1 & 1 \\ -2 & 1 \end{bmatrix} \]

**Solution for X:**

\[ X = \begin{bmatrix} \text{(Enter your solution here)} \\ \text{(Enter your solution here)} \end{bmatrix} \]

### Problem 2: Solve for Y

**Given Matrix Equation:**

\[ AY = \begin{bmatrix} -10 \\ -20 \end{bmatrix} \]

**Solution for Y:**

\[ Y = \begin{bmatrix} \text{(Enter your solution here)} \\ \text{(Enter your solution here)} \end{bmatrix} \]
Transcribed Image Text:## Matrix Equation Solutions ### Problem 1: Solve for X **Given Matrix Equation:** \[ AX = \begin{bmatrix} 3 \\ 15 \end{bmatrix} \] To solve for \( X \), use the inverse of matrix \( A \): \[ A^{-1} = \begin{bmatrix} -1 & 1 \\ -2 & 1 \end{bmatrix} \] **Solution for X:** \[ X = \begin{bmatrix} \text{(Enter your solution here)} \\ \text{(Enter your solution here)} \end{bmatrix} \] ### Problem 2: Solve for Y **Given Matrix Equation:** \[ AY = \begin{bmatrix} -10 \\ -20 \end{bmatrix} \] **Solution for Y:** \[ Y = \begin{bmatrix} \text{(Enter your solution here)} \\ \text{(Enter your solution here)} \end{bmatrix} \]
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