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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Question
![**Matrix Equation Solving**
To solve for the matrix \( X \), we are given two matrices \( A \) and \( B \):
\[ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \]
\[ B = \begin{bmatrix} 1 & 1 \\ -1 & 0 \end{bmatrix} \]
The equation provided is:
\[ 3(A - B + X) = 4(X - A) \]
We need to solve this equation to find the values for the matrix \( X \):
\[ X = \begin{bmatrix} \text{[ ]} & \text{[ ]} \\ \text{[ ]} & \text{[ ]} \end{bmatrix} \]
**Explanation of Approach:**
To solve for \( X \), follow these steps:
1. **Distribute and simplify the equation**:
- Distribute the 3 and the 4 in respective terms.
- Combine like terms to isolate \( X \).
2. **Solve for the matrix \( X \)**:
- After simplification, deduce the values that satisfy the equation for each element in the matrix \( X \).
This process involves basic matrix operations such as addition, subtraction, and scalar multiplication. Solving for \( X \) requires manipulation and careful handling of the equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8fa7aa4-dafc-4c07-b274-462aa6ff800c%2F8f9877c7-ce12-41d9-a9b7-c4327ea322eb%2Fvnay4x9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Equation Solving**
To solve for the matrix \( X \), we are given two matrices \( A \) and \( B \):
\[ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \]
\[ B = \begin{bmatrix} 1 & 1 \\ -1 & 0 \end{bmatrix} \]
The equation provided is:
\[ 3(A - B + X) = 4(X - A) \]
We need to solve this equation to find the values for the matrix \( X \):
\[ X = \begin{bmatrix} \text{[ ]} & \text{[ ]} \\ \text{[ ]} & \text{[ ]} \end{bmatrix} \]
**Explanation of Approach:**
To solve for \( X \), follow these steps:
1. **Distribute and simplify the equation**:
- Distribute the 3 and the 4 in respective terms.
- Combine like terms to isolate \( X \).
2. **Solve for the matrix \( X \)**:
- After simplification, deduce the values that satisfy the equation for each element in the matrix \( X \).
This process involves basic matrix operations such as addition, subtraction, and scalar multiplication. Solving for \( X \) requires manipulation and careful handling of the equations.
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