Solve the equation for x, y, z and t, if `2[[x ,z ],[y ,t]]+3[[1,-1 ],[0 ,2]]=3[[3 ,5 ],[4 ,6]]`

Explanation

To solve the equation \( 2\begin{bmatrix} x & z \\ y & t \end{bmatrix} + 3\begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} = 3\begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix} \), we will follow these steps:

### Step 1: Multiply the matrices by their respective scalars

First, we will multiply the matrix \( \begin{bmatrix} x & z \\ y & t \end{bmatrix} \) by 2 and the matrix \( \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} \) by 3.

\[
2\begin{bmatrix} x & z \\ y & t \end{bmatrix} = \begin{bmatrix} 2x & 2z \\ 2y & 2t \end{bmatrix}
...