Given `A=[[1,-1, 0], [2, 3, 4], [0, 1, 2]], B= [[2,2,-4],[-4,2,-4],[2,-1,5]]` find AB and use this to solve the system of equations: `y+2x=7,x-y=3,2x+3y+4z=17`

Explanation

To solve the given problem, we will first find the product of matrices A and B, and then use that result to solve the system of equations.

### Step 1: Define the Matrices
Given:
\[ A = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \]
\[ B = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 & -1 & 5 \end{bmatrix} \]

### Step 2: Multiply Matrices A and B
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