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Question

# Solve the matrix equation for X. [1 -1 1, 2 3 0, 0 2 -1] X = [2 - 1 5 7 8, 4 0 -3, 0 1, 3 5 -7 2 1]

Solution

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Step 1
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Given that:

$\begin{bmatrix} 1&-1&1 \\ 2 & 3& 0\\0 &2&-1 \end{bmatrix}$

X =

$\begin{bmatrix} 2&-1&5 &7 &8 \\ 4 & 0& -3 & 0 &1\\3 &5&-7 &2 &1 \end{bmatrix}$

We need to solve for X:

Suppose the matrix on the left hand side of X is called A.

Then AX =

$\begin{bmatrix} 2&-1&5 &7 &8 \\ 4 & 0& -3 & 0 &1\\3 &5&-7 &2 &1 \end{bmatrix}$

Then X=

$A^{-1} \begin{bmatrix} 2&-1&5 &7 &8 \\ 4 & 0& -3 & 0 &1\\3 &5&-7 &2 &1 \end{bmatrix}$

Then we need to get the matrix $A^{-1}$ first.

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