1. Solve matrix equation A· X = B using the methods of your choice. Clearly mark the answers. Question a. 1 -1 1 A = -1 1 В — -1 3 1 Question b. 1 2 1 A = 1 1 В — 1 2 Question c. 1 0 1 1 A = 0 1 1 В 1 1 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please solve only question 2.

## Solve Matrix Equation \( A \cdot X = B \)

### Instructions:
Solve the matrix equation \( A \cdot X = B \) using the methods of your choice. Clearly mark the answers.

---

### Question a

Given matrices:
\[ 
A = \begin{bmatrix}
1 & -1 \\
-1 & 1 \\
2 & 3
\end{bmatrix}, 
\quad
B = \begin{bmatrix}
1 \\
-1 \\
1
\end{bmatrix}
\]

### Question b

Given matrices:
\[ 
A = \begin{bmatrix}
1 & 2 & 1 \\
1 & 1 & 2
\end{bmatrix}, 
\quad
B = \begin{bmatrix}
1 \\
0
\end{bmatrix}
\]

### Question c

Given matrices:
\[ 
A = \begin{bmatrix}
1 & 0 & 1 \\
0 & 1 & 1 \\
1 & 1 & 0
\end{bmatrix}, 
\quad
B = \begin{bmatrix}
1 \\
1 \\
0
\end{bmatrix}
\]

---

Note: You may use methods such as row reduction, inverse matrices, or any other appropriate techniques to find the solution \( X \). Make sure to explicitly show all steps and calculations involved in solving for \( X \) in each question.
Transcribed Image Text:## Solve Matrix Equation \( A \cdot X = B \) ### Instructions: Solve the matrix equation \( A \cdot X = B \) using the methods of your choice. Clearly mark the answers. --- ### Question a Given matrices: \[ A = \begin{bmatrix} 1 & -1 \\ -1 & 1 \\ 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 1 \\ -1 \\ 1 \end{bmatrix} \] ### Question b Given matrices: \[ A = \begin{bmatrix} 1 & 2 & 1 \\ 1 & 1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 1 \\ 0 \end{bmatrix} \] ### Question c Given matrices: \[ A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{bmatrix}, \quad B = \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} \] --- Note: You may use methods such as row reduction, inverse matrices, or any other appropriate techniques to find the solution \( X \). Make sure to explicitly show all steps and calculations involved in solving for \( X \) in each question.
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