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Find the value of a, b, c and d, if 3\(\begin{bmatrix} a & b \\[0.3em] c & d \end{bmatrix}\) = \(\begin{bmatrix} a & 6 \\[0.3em] -1 & 2d \end{bmatrix}\) + \(\begin{bmatrix} 4 &a+ b \\[0.3em] c+d & 3 \end{bmatrix}\).

1 Answer

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Best answer

Given,

As both matrices are equal so their corresponding elements must also be equal.

∴ 3a = a + 4

⇒ 2a = 4

⇒ a = 2

Similarly,

3b = 6 + a + b

⇒ 2b = 6 + a

As from above a = 2

∴ 2b = 6+2 = 8

⇒ b = 4

Also 3d = 2d + 3

⇒ d = 3

And,

3c = -1 + c + d

⇒ 2c = d – 1

⇒ 2c = 3-1

⇒ c = 2/2 = 1

Thus a = 2, b = 4, c = 1 and d = 3.

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