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,...
Related questions
Question
![**Solve for \( X \).**
The equation to solve is given by:
\[
\begin{bmatrix}
-1 & 5 & 8 \\
-3 & -1 & 3
\end{bmatrix}
=
-4X + 4
\begin{bmatrix}
-1 & 1 & -2 \\
5 & -3 & 4
\end{bmatrix}
\]
To solve, you will perform matrix operations to find the matrix \( X \).
Below the equation, there are two empty matrices, indicating the solution for matrix \( X \) should be entered.
**Explanation:**
- The matrix on the left side of the equation:
\[
\begin{bmatrix}
-1 & 5 & 8 \\
-3 & -1 & 3
\end{bmatrix}
\]
- The expression on the right side involves a scalar multiplication of \( -4 \) with the unknown matrix \( X \), added to a scaled matrix by a factor of \( 4 \):
\[
4
\begin{bmatrix}
-1 & 1 & -2 \\
5 & -3 & 4
\end{bmatrix}
\]
Your task is to solve for the matrix \( X \) that satisfies this equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf673b33-84d3-4207-a3d8-77b439e8ab65%2Fab6e795b-0b78-457e-9acd-2f2e07c87683%2F8zz1wzr_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve for \( X \).**
The equation to solve is given by:
\[
\begin{bmatrix}
-1 & 5 & 8 \\
-3 & -1 & 3
\end{bmatrix}
=
-4X + 4
\begin{bmatrix}
-1 & 1 & -2 \\
5 & -3 & 4
\end{bmatrix}
\]
To solve, you will perform matrix operations to find the matrix \( X \).
Below the equation, there are two empty matrices, indicating the solution for matrix \( X \) should be entered.
**Explanation:**
- The matrix on the left side of the equation:
\[
\begin{bmatrix}
-1 & 5 & 8 \\
-3 & -1 & 3
\end{bmatrix}
\]
- The expression on the right side involves a scalar multiplication of \( -4 \) with the unknown matrix \( X \), added to a scaled matrix by a factor of \( 4 \):
\[
4
\begin{bmatrix}
-1 & 1 & -2 \\
5 & -3 & 4
\end{bmatrix}
\]
Your task is to solve for the matrix \( X \) that satisfies this equation.
Expert Solution
Step 1: Concept
We solve the matrix equations in the same way as any other algebraic equations, except in matrix equations we use matrix sum and difference, and scalar multiplication.
Step by step
Solved in 3 steps with 2 images
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