If $\mathrm{A}=\left[\begin{array}{lll}1 & 1 & 1 \ 1 & \mathrm{a} & 3 \ 3 & 2 & 2\end{array} ight]$ and $\mathrm{B}=\left[\begin{array}{ccc}-2 & 0 & \mathrm{~b} \ 7 & -1 & -2 \ \mathrm{c} & 1 & 1\end{array} ight]$ and if matrix $B$ is the inverse of matrix $A$, then value of $4 a+2 b-c$ is

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If $\mathrm{A}=\left[\begin{array}{lll}1 & 1 & 1 \ 1 & \mathrm{a} & 3 \ 3 & 2 & 2\end{array}ight]$ and $\mathrm{B}=\left[\begin{array}{ccc}-2 & 0 & \mathrm{~b} \ 7 & -1 & -2 \ \mathrm{c} & 1 & 1\end{array}ight]$ and if matrix $B$ is the inverse of matrix $A$, then value of $4 a+2 b-c$ is

Aicharya · Accepted Answer

$\begin{aligned} & B=A^{-1} \ & {\left[\begin{array}{ccc}-2 & 0 & b \ 7 & -1 & -2 \ c & 1 & 1\end{array}ight]=A^{-1}} \ & {\left[\begin{array}{ccc}-2 & 0 & b \ 7 & -1 & -2 \ c & 1 & 1\end{array}ight] A=A^{-1} A} \ & {\left[\begin{array}{ccc}-2 & 0 & b \ 7 & -1 & -2 \ c & 1 & 1\end{array}ight]\left[\begin{array}{ccc}1 & 1 & 1 \ 1 & a & 3 \ 3 & 2 & 2\end{array}ight]=I}\end{aligned}$ $\left[\begin{array}{ccc}-2+3 b & -2+2 b & -2+2 b \ 7-1-6 & 7-a-4 & 7-3-4 \ c+1+3 & c+a+2 & c+3+2\end{array}ight]=\left[\begin{array}{ccc}1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1\end{array}ight]$ On equality of matrix, $-2+3 b=1,7-a-4=1, c+3+2=1$ $\begin{aligned} \Rightarrow b=1, a & =2, c=-4 \ 	herefore \quad 4 a+2 b-c & =4(2)+2(1)+4 \ & =8+2+4=14\end{aligned}$

If $\mathrm{A}=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & \mathrm{a} & 3 \\ 3 & 2 & 2\end{array}\right]$ and…

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