Question

Find x, y, z, if `{5[(0, 1),(1, 0),(1, 1)] - [(2, 1),(3, - 2),(1, 3)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`

Answer 1

`{5[(0, 1),(1, 0),(1, 1)] - [(2, 1),(3, - 2),(1, 3)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`

∴ `{[(0, 5),(5, 0),(5, 5)] - [(2, 1),(3, - 2),(1, 3)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`

∴ `[(0 - 2,  - 1),(5 - 3, 0 + 2),(5 - 1,  - 3)][(2),(1)] = [(x - 1),(y + 1),(2z)]`

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

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

∴ `[(0),(6),(10)] = [(x - 1),(y + 1),(2z)]`

∴ By equality of matrices, we get
x  – 1 = 0 

∴ x = 1

y + 1 = 6

∴ y = 5

z = 10

∴ z = 5