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Question

If A=-123x2y4-1650 is a symmetric matrix, then the value of 2x + y is ___________.

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Solution


A matrix X is a symmetric matrix if XT = X.

It is given that, the matrix A=-123x2y4-1650 is a symmetric matrix.
AT=A

-123x2y4-1650T=-123x2y4-1650

-12y62453x-10=-123x2y4-1650

⇒ 3x = 6 and 2y = 2

⇒ x = 2 and y = 1

∴ 2x + y = 2 × 2 + 1 = 5

Thus, the value of 2x + y is 5.

If A=-123x2y4-1650 is a symmetric matrix, then the value of 2x + y is _____5_____.


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