https://file.aiquickdraw.com/mathbot/file/1728440649690u0bsahth.jpg

The equation presented in the image involves a system of matrix equations. Here's how it breaks down:

\[
\begin{bmatrix} 
2 & 1 \\
3 & 4 
\end{bmatrix} X = \left( \begin{bmatrix} 5 & 0 \\ 1 & -2 \end{bmatrix} - 2 \cdot \begin{bmatrix} 4 & -1 \\ 4 & 0 \end{bmatrix} \right) X
\]

### Steps to solve for \(X\):

1. **Simplify the right-hand side:**
   - Start by multiplying the second matrix by 2.
     \[
     2 \cdot \begin{bmatrix} 4 & -1 \\ 4 & 0 \end{bmatrix} = \begin{bmatrix} 8 & -2 \\ 8 & 0 \end{bmatrix}
     \]
   - Now subtract this from the first matrix on the right-hand side:
     \[
     \begin{bmatrix} 5 & 0 \\ 1 & -2 \end{bmatrix} - \begin{bmatrix} 8 & -2 \\ 8 & 0 \end{bmatrix} = \begin{bmatrix} -3 & 2 \\ -7 & -2 \end{bmatrix}
     \]
   
   So the equation becomes:
   \[
   \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} X = \begin{bmatrix} -3 & 2 \\ -7 & -2 \end{bmatrix} X


Find matrix X given the equation [2 1; 3 4] X = ([5 0; 1 -2] - 2 * [4 -1; 4 0]) X

Learn how to solve a matrix equation where two matrices are subtracted and multiplied. This problem involves key linear algebra concepts, such as matrix operations and matrix equations, suitable for undergraduate students.

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