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Find the Value Of A, B, C, And D From the Equation: [(A-b, 2a+C),(2a-b, 3x+D)] = [(-1,5),(0,13)] - CBSE (Science) Class 12 - Mathematics

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Question

Find the value of abc, 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:

− 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 + = 13 ⇒ d = 4

a = 1, b = 2, c = 3, and d = 4

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Solution Find the Value Of A, B, C, And D From the Equation: [(A-b, 2a+C),(2a-b, 3x+D)] = [(-1,5),(0,13)] Concept: Types of Matrices.
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