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Let $\mathrm{A}=\left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1\end{array}\right], \mathrm{B}=\left[\begin{array}{c}6 \\ 11 \\ 0\end{array}\right]$ and $\mathrm{X}-\left[\begin{array}{l}\mathrm{a} \\ \mathrm{b} \\ \mathrm{c}\end{array}\right]$, if $\mathrm{AX}=\mathrm{B}$, then the value of $2 \mathrm{a}+\mathrm{b}+2 \mathrm{c}$ is
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10
$\begin{aligned} & \mathrm{AX}=\mathrm{B} \\ & {\left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1\end{array}\right]\left[\begin{array}{l}a \\ b \\ c\end{array}\right]=\left[\begin{array}{c}6 \\ 11 \\ 0\end{array}\right]} \\ & \therefore \quad a+b+c=6 ...(i)\\ & \mathrm{~b}+3 \mathrm{c}=11 ...(ii)\\ & a-2 b+c=0 \\ & \text { i.e., } a+c=2 b ...(iii)\\ & \text { From (i) and (ii), we get } b=2 \\ & \text { From (ii), } c=3 \\ & \text { From (i), } a=1 \\ & \therefore \quad 2 \mathrm{a}+\mathrm{b}+2 \mathrm{c}=2(1)+2+2(3)=10 \\ & \end{aligned}$
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