Question

Find the x, y, z, if `{3[(2,0),(0,2),(2,2)]-4[(1,1),(-1,2),(3,1)]}[(1),(2)]=[(x-3),(y-1),(      2z)]`

Answer 1

`{3[(2,0),(0,2),(2,2)]-4[(1,1),(-1,2),(3,1)]}[(1),(2)]=[(x-3),(y-1),(      2z)]`

∴`{[(6,0),(0,6),(6,6)]-[(4,4),(-4,8),(12,4)]}[(1),(2)]=[(x-3),(y-1),(      2z)]`

∴`[(2,-4),(4,-2),(-6,2)][(1),(2)] =[(x-3),(y-1),(      2z)]`

∴`[(2-8),(4-4),(-6+4)]=[(x-3),(y-1),(      2z)]`

∴ `[(-6),(0),(-2)]=[(x-3),(y-1),(      2z)]`

By equality of matrices

-6 = x - 3, 0 = y - 1 and -2 = 2z

∴ x = -3, y = 1 and z = -1