Let $\mathrm{A}=\left[\begin{array}{ccc}1 & 1 & 1 \ 0 & 1 & 3 \ 1 & -2 & 1\end{array} ight], \mathrm{B}=\left[\begin{array}{c}6 \ 11 \ 0\end{array} ight]$ and $\mathrm{X}-\left[\begin{array}{l}\mathrm{a} \ \mathrm{b} \ \mathrm{c}\end{array} ight]$, if $\mathrm{AX}=\mathrm{B}$, then the…

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Let $\mathrm{A}=\left[\begin{array}{ccc}1 & 1 & 1 \ 0 & 1 & 3 \ 1 & -2 & 1\end{array}ight], \mathrm{B}=\left[\begin{array}{c}6 \ 11 \ 0\end{array}ight]$ and $\mathrm{X}-\left[\begin{array}{l}\mathrm{a} \ \mathrm{b} \ \mathrm{c}\end{array}ight]$, if $\mathrm{AX}=\mathrm{B}$, then the value of $2 \mathrm{a}+\mathrm{b}+2 \mathrm{c}$ is

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{AX}=\mathrm{B} \ & {\left[\begin{array}{ccc}1 & 1 & 1 \ 0 & 1 & 3 \ 1 & -2 & 1\end{array}ight]\left[\begin{array}{l}a \ b \ c\end{array}ight]=\left[\begin{array}{c}6 \ 11 \ 0\end{array}ight]} \ & 	herefore \quad a+b+c=6 ...(i)\ & \mathrm{~b}+3 \mathrm{c}=11 ...(ii)\ & a-2 b+c=0 \ & 	ext { i.e., } a+c=2 b ...(iii)\ & 	ext { From (i) and (ii), we get } b=2 \ & 	ext { From (ii), } c=3 \ & 	ext { From (i), } a=1 \ & 	herefore \quad 2 \mathrm{a}+\mathrm{b}+2 \mathrm{c}=2(1)+2+2(3)=10 \ & \end{aligned}$

Let $\mathrm{A}=\left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1\end{array}\right],…

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