Q. 6 B4.3( 79 Votes )
Find the values of x, y and z from the following equations:
Answer :
Since, the given matrices are equal, their corresponding elements are also equal.
Comparing the corresponding element, we have:
x + y = 6, xy = 8, 5 + z = 5
Now, 5 + z = 5
⇒ z = 0
x+ y = 6
⇒ x = 6 - y
Also,
xy = 8
⇒ (6 - y)y = 8
⇒ 6y - y2 = 8
⇒ y2 - 6y + 8 = 0
⇒ y2 - 4y - 2y + 8 = 0
⇒ y(y - 4) - 2(y - 4) = 0
⇒ (y - 2)(y - 4) = 0
Hence, y = 2 or y = 4
when y = 2
x = 6 - 2 = 4
when x = 4
x = 6 - 4 = 2
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