If (Q ) is the inverse of (A ), when (A= [ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array ] ) and (10 Q= [ array ccc 4 & 2 & 2 -5 & 0 & x 1 & -2 & 3 array ] ), find (x= )

Step-by-step solution

Given, (Q=A⁻¹ ) ( aligned A & = [ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array ] |A| & =1(1+3)+1(2+3)+1(2-1)=4+5+1 |A| & =10 aligned ) ( Adj A= [ array ccc 4 & -5 & 1 2 & 0 & -2 2 & 5 & 3 array ]^ T ) Adj (A= [ array ccc 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 array ] ) ( aligned & A⁻¹= 1 | ~A | Adj A & A⁻¹= 1 10 [ array rrr 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 array ] & 10 Q= [ array rrr 4 & 2 & 2 -5 & 0 & x 1 & -2 & 3 array ] & 10 A⁻¹= [ array rrr 4 & 2 & 2 -5 & 0 & x 1 & -2 & 3 array ] & [ array rrr 4 & 2 & 2 -5 & 0 & 5 1