Given $\mathrm{A}=\left[\begin{array}{lll}x & 3 & 2 \ 1 & y & 4 \ 2 & 2 & z\end{array} ight], x y z=60$ and $8 x+4 y+3 z=20$, then $\mathrm{A} \cdot(\operatorname{adjA})$ is equal to

Question

Given $\mathrm{A}=\left[\begin{array}{lll}x & 3 & 2 \ 1 & y & 4 \ 2 & 2 & z\end{array}ight], x y z=60$ and $8 x+4 y+3 z=20$, then $\mathrm{A} \cdot(\operatorname{adjA})$ is equal to

Aicharya · Accepted Answer

$\begin{aligned} & |A|=x(y z-8)+3(8-z)+2(2-2 y) \ & =x y z-8 x+24-3 z+4-4 y \ & =x y z-(8 x+4 y+3 z)+28 \ & =60-20+28 \ & =68 \end{aligned}$ we have, $A \cdot \operatorname{adj}(A)=|A| I=\left[\begin{array}{ccc}68 & 0 & 0 \ 0 & 68 & 0 \ 0 & 0 & 68\end{array}ight]$

Given $\mathrm{A}=\left[\begin{array}{lll}x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z\end{array}\right], x y z=60$…

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