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GATE 2022 ME (ME1) – Question 15

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors · 1 mark · Multiple choice

If $\mathbf{A} = \begin{bmatrix} 10 & 2k + 5 \\ 3k - 3 & k + 5 \end{bmatrix}$ is a symmetric matrix, the value of $k$ is ___________.

  1. 8
  2. 5
  3. −0.4
  4. $\frac{1 + \sqrt{1561}}{12}$

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Correct answer: (A) 8

Explanation

A symmetric matrix has equal off-diagonal entries: $2k + 5 = 3k - 3$, so $k = 8$.