Solve the matrix equation AX = B for X. A = X = 15 -25 B= 30 15
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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![**Problem Statement:**
Solve the matrix equation \( AX = B \) for \( X \).
**Given Matrices:**
\[
A = \begin{bmatrix} 1 & 5 \\ -2 & 5 \end{bmatrix}, \quad B = \begin{bmatrix} 30 \\ 15 \end{bmatrix}
\]
**Solution:**
\( X = \begin{bmatrix} \Box \\ \Box \end{bmatrix} \)
**Explanation:**
You are given a system of linear equations represented in the form of matrices. Matrix \( A \) is a 2x2 matrix, and matrix \( B \) is a 2x1 column matrix. You need to find the 2x1 column matrix \( X \) that satisfies the equation \( AX = B \).
1. **Matrix \( A \):**
- First row: 1, 5
- Second row: -2, 5
2. **Matrix \( B \):**
- First row: 30
- Second row: 15
3. **Matrix \( X \):**
- Consists of unknowns to be solved for.
To solve for \( X \), you will typically use methods such as matrix inversion or other algebraic techniques suitable for 2x2 matrices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09ace70e-38b4-4990-b7ba-acac1bf1dd80%2F8a89517e-596d-4f21-8c3a-b2003599f882%2F66u5net_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the matrix equation \( AX = B \) for \( X \).
**Given Matrices:**
\[
A = \begin{bmatrix} 1 & 5 \\ -2 & 5 \end{bmatrix}, \quad B = \begin{bmatrix} 30 \\ 15 \end{bmatrix}
\]
**Solution:**
\( X = \begin{bmatrix} \Box \\ \Box \end{bmatrix} \)
**Explanation:**
You are given a system of linear equations represented in the form of matrices. Matrix \( A \) is a 2x2 matrix, and matrix \( B \) is a 2x1 column matrix. You need to find the 2x1 column matrix \( X \) that satisfies the equation \( AX = B \).
1. **Matrix \( A \):**
- First row: 1, 5
- Second row: -2, 5
2. **Matrix \( B \):**
- First row: 30
- Second row: 15
3. **Matrix \( X \):**
- Consists of unknowns to be solved for.
To solve for \( X \), you will typically use methods such as matrix inversion or other algebraic techniques suitable for 2x2 matrices.
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