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If \(A=\begin{bmatrix} 1 &-1 & 0 \\[0.3em] 2 & 3 & 4 \\[0.3em] 0 & 1 &2 \end{bmatrix}\)\(B=\begin{bmatrix} 2 &2 & -4 \\[0.3em] -4 & 2 & -4 \\[0.3em] 2 & -1 &5 \end{bmatrix}\) are two square matrices, find AB and hence solve the following system of linear equations :

x – y = 3, 2x + 3y + 4z = 17 and y + 2z = 7

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Best answer

We have,

\(A=\begin{bmatrix} 1 &-1 & 0 \\[0.3em] 2 & 3 & 4 \\[0.3em] 0 & 1 &2 \end{bmatrix}\)\(B=\begin{bmatrix} 2 &2 & -4 \\[0.3em] -4 & 2 & -4 \\[0.3em] 2 & -1 &5 \end{bmatrix}\)

Now,

The given system of linear equations can be written in matrix form as,

AX = B,

Where,

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