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# Solve for x : $\begin{bmatrix} 1 - x & 1 \end{bmatrix} \begin{bmatrix} 2 & -1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 3 \end{bmatrix} = 0$

Toolbox:
• If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B: $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$
Step1:
Given:
$\begin{bmatrix}1 - x& 1\end{bmatrix}\begin{bmatrix}2 & -1\\1 & 2\end{bmatrix}\begin{bmatrix}1\\3\end{bmatrix}$=0
$\begin{bmatrix}1 - x& 1\end{bmatrix}\begin{bmatrix}2(1)+3(-1)\\1(1)+2(3)\end{bmatrix}=0$
$\begin{bmatrix}1-x &1\end{bmatrix}\begin{bmatrix}-1\\7\end{bmatrix}$=0
Step2:
(1-x)-1+1(7)=0.
-1+x+7=0.
x+6=0
x=-6