Let A= [ array cc x+y & y 2 x & x-y array ], B= [ array c 2 -1 array ] and C= [ array l 3 2 array ] . If A B=C , then what is the value of the determinant of the matrix A ?

Step-by-step solution

aligned A B & = [ array cc x+y & y 2 x & x-y array ] [ array c 2 -1 array ] & = [ array c 2(x+y)-y 4 x-x+y array ]= [ array l 2 x+y 3 x+y array ] aligned As A B=C aligned & [ array l 2 x+y 3 x+y array ]= [ array l 3 2 array ] & 2 x+y=3 (i) aligned and 3 x+y=2 (ii) From equation (i) and (ii), we get x=-1, y=5 . aligned A & = [ array cc -1+5 & 5 -2 & -1-5 array ]= [ array cc 4 & 5 -2 & -6 array ] & =4(-6)-5(-2)=-14 aligned