Find x, if \(\begin{bmatrix} x &-5&-1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 0 & 2\\ 0 & 2 & 1 \\2&1&3 \end{bmatrix}\)\(\begin{bmatrix} x \\ 4\\1 \end{bmatrix}=O\)
Solution and Explanation
We have \(\begin{bmatrix} x &-5&-1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 0 & 2\\ 0 & 2 & 1 \\2&1&3 \end{bmatrix}\)\(\begin{bmatrix} x \\ 4\\1 \end{bmatrix}=O\)
⇒ \(\begin{bmatrix} x+0-2 &0-10+-0 &2x-5-3\end{bmatrix}\) \(\begin{bmatrix} x \\ 4\\1 \end{bmatrix}=O\)
⇒ \(\begin{bmatrix} x-2 &-10&2x-8 \end{bmatrix}\) \(\begin{bmatrix} x \\ 4\\1 \end{bmatrix}=O\)
⇒ \(\begin{bmatrix} x(x-2) -40+2x-8 \end{bmatrix}=0\)
⇒ \(\begin{bmatrix} x^2 -2x-40+2x-8 \end{bmatrix}=[0]\)
⇒ \(\begin{bmatrix} x^2 -48 \end{bmatrix}=[0]\)
⇒\(\therefore x^2=48\)
⇒ \(x= 4 \sqrt3\)
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