Question

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

Answer 1

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

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

∴ `[(8 - 3, -4 + 3, 12 - 4),(4 - 2, 0 - 1, 8 - 1)][(2),(-1),(1)] = [(x),(y)]`

∴ `[(5,-1, 8),(2, -1, 7)][(2),(-1),(1)] = [(x),(y)]`

∴ `[(10 + 1 + 8),(4 + 1 + 7)] = [(x),(y)]`

∴ `[(19),(12)] = [(x),(y)]`

∴ By equality of matrices, we get
x = 19 and y = 12.