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Question
Find the value of x, y and z from the following equation:
`[(x + y, 2),(5 + z, xy)] = [(6, 2), (5, 8)]`
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Solution
`[(x + y, 2),(5 + z, xy)] = [(6, 2), (5, 8)]`
As the given matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get:
x + y = 6, xy = 8, 5 + z = 5
Now, 5 + z = 5 ⇒ z = 0
We know that:
(x – y)2 = (x + y)2 – 4xy
⇒ (x – y)2 = 36 – 32 = 4
⇒ x – y = ±2
Now, when x – y = 2 and x + y = 6, we get x = 4 and y = 2
When x – y = –2 and x + y = 6, we get x = 2 and y = 4
∴ x = 4, y = 2 and z = 0 or x = 2, y = 4 and z = 0
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