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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:
Now, 5 + z = 5 ⇒ z = 0
Also, x + y = 6
y = 6 - x .....(i)
and xy = 8 .....(ii)
Solving (i) & (ii), we have x (6 - x) = 8
= 6x - x2 = 8
x2 - 6x + 8 = 0
= (x - 4) (x - 2) = 0
= x = 2, 4
When x = 2, we get y = 4 and when x = 4, we get y = 6 - 4 = 2
Hence, x = 2, y = 4, z = 0 or x = 4, y = 2, z = 0.
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