Question

If X = `[(8,-1,-3),(-5,1,2),(10,-1,-4)]` and Y = `[(2,1,-1),(0,2,1),(5,p,q)]`  then, find p, q if Y = X^-1

Answer 1

Given that Y is the inverse of X.

∴ XY = I

`[(8,-1,-3),(-5,1,2),(10,-1,-4)][(2,1,-1),(0,2,1),(5,p,q)] = [(1,0,0),(0,1,0),(0,0,1)]`

`[(16-0-15,8-2-3p,-8-1-3q),(-10+0+10,-5+2+2p,5+1+2q),(20-0-20,10-2-4p,-10-1-4q)] = [(1,0,0),(0,1,0),(0,0,1)]`

`[(1,6-3p,-9-3q),(0,-3+2p,6+2q),(0,8-4p,-11-4q)] = [(1,0,0),(0,1,0),(0,0,1)]`

6 – 3p = 0 and -9 – 3q = 0

6 = 3p and -9 = 3q

∴ p = 2; q = - 3