If A = [ array lll 1 & 1 & 1 1 & a & 3 3 & 2 & 2 array ] and B = [ array ccc -2 & 0 & ~b 7 & -1 & -2 c & 1 & 1 array ] and if matrix B is the inverse of matrix A , then value of 4 a+2 b-c is

Step-by-step solution

aligned & B=A⁻¹ & [ array ccc -2 & 0 & b 7 & -1 & -2 c & 1 & 1 array ]=A⁻¹ & [ array ccc -2 & 0 & b 7 & -1 & -2 c & 1 & 1 array ] A=A⁻¹ A & [ array ccc -2 & 0 & b 7 & -1 & -2 c & 1 & 1 array ] [ array ccc 1 & 1 & 1 1 & a & 3 3 & 2 & 2 array ]=I aligned [ 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 array ]= [ array ccc 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] On equality of matrix, -2+3 b=1,7-a-4=1, c+3+2=1 aligned b=1, a & =2, c=-4 4 a+2 b-c & =4(2)+2(1)+4 & =8+2+4=14 aligned