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

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