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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), (3z)]`
Solution
`{5[(0, 1),(1, 0),(1, 1)] - [(2, 1),(3, -2),(1, 3)]}[(2),(1)] = [(x + 1),(y - 1), (3z)]`
⇒ `{[(0, 5),(5, 0),(5, 5)] - [(2, 1),(3, -2),(1, 3)]}[(2),(1)] = [(x + 1),(y - 1),(3z)]`
⇒ `[(-2, 4),(2, 2),(4, 2)][(2),(1)] = [(x + 1),(y - 1),(3z)]`
⇒ `[(-4 + 4),(4 + 2),(8 + 2)] = [(x + 1),(y - 1),(3z)]`
⇒ `[(0),(6),(10)] = [(x + 1),(y - 1),(3z)]`
∴ By equality of matrices. we get
x + 1 = 0 ⇒ x = – 1
y – 1 = 6 ⇒ y = 7
3z = 10 ⇒ z = `10/3`
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