If X=[[|gathered x y z gathered]]| is a solution of the system of equations AX=B, where ad…

Question

If $X=[[|\begin{gathered} x \ y \ z \end{gathered}]]|$ is a solution of the system of equations $AX=B$, where $adjA=[[|\begin{gathered} 4 \quad  2 \quad  2 \ -5 \quad  0 \quad  5 \ 1 \quad  -2 \quad  3 \end{gathered}]]|$ and $B=[[|\begin{gathered} 4 \ 0 \ 2 \end{gathered}]]|$, then $|x+y+z|$ is equal to :

Accepted Answer

$\begin{gathered} X \quad  ={A}^{-1}B=(\frac{adjA}{|A|})B=\pm \frac{1}{10}((|\begin{array}{ccc}4 \quad  2 \quad  2 \ -5 \quad  0 \quad  5 \ 1 \quad  -2 \quad  3\end{array}))|((|\begin{array}{cc}4 \ 0 \ 2\end{array}))|=\pm \frac{1}{10}((|\begin{array}{cc}20 \ -10 \ 10\end{array}))|=\pm ((|\begin{array}{cc}2 \ -1 \ 1\end{array}))| \ 	herefore |x+y+z|=2 \end{gathered}$

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