Solving Matrix Equations: X from a System Involving Scalar Multiplication

Math Problem Statement

Solve for X given the matrix equation: [ [ 5, -8, 5 ], [ 8, -5, 4 ] ] = 3X - 3[ [ -5, 4, 3 ], [ -4, -6, -8 ] ]

It seems there was an issue accessing the image. However, I can solve the problem directly by interpreting the equation in the image.

The matrix equation is given as:

5 & -8 & 5 \\ 8 & -5 & 4 \end{bmatrix} = 3X - 3\begin{bmatrix} -5 & 4 & 3 \\ -4 & -6 & -8 \end{bmatrix}$$ We can isolate $$X$$ by manipulating this equation. Let me go ahead and solve it. The steps involve: 1. Adding the second matrix to both sides. 2. Dividing by 3 to isolate $$X$$. Let's compute it now.The solution for $$X$$ is: $$X = \begin{bmatrix} -3.33 & 1.33 & 4.67 \\ -1.33 & -7.67 & -6.67 \end{bmatrix}$$ Would you like further details on how this was computed, or have any questions? Here are some related questions you may find helpful: 1. What is the general method for solving matrix equations? 2. How do you multiply a scalar by a matrix? 3. What are some common applications of matrix operations? 4. How do you solve systems of linear equations using matrices? 5. How can you verify the solution to a matrix equation? **Tip:** When working with matrix equations, always ensure the matrix dimensions match when performing addition or multiplication!

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