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Question
Find the value of a, b, c, and d from the equation:
`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`
Solution
`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`
As the two matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get:
a − b = −1 ....(1)
2a − b = 0 ....(2)
2a + c = 5 ....(3)
3c + d = 13 ...(4)
From (2), we have:
b = 2a
Then, from (1), we have:
a − 2a = −1
⇒ a = 1
⇒ b = 2
Now, from (3), we have:
2 ×1 + c = 5
⇒ c = 3
From (4) we have:
3 ×3 + d = 13
⇒ 9 + d = 13
⇒ d = 4
∴ a = 1, b = 2, c = 3, and d = 4
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