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COMEDK202510 May 2025Evening ShiftMathematicsMatricesActual

If A= [ array ccc 0 & -1 & 2 1 & 0 & 3 -2 & -3 & 0 array ] , then A+2 A^T=

Options

  1. A2 A^2
  2. BA
  3. C-A^T
  4. DA^T

Correct answer

D. A^T

Step-by-step solution

Given the matrix A = bmatrix 0 & -1 & 2 1 & 0 & 3 -2 & -3 & 0 bmatrix . The transpose of matrix A is A^T = bmatrix 0 & 1 & -2 -1 & 0 & -3 2 & 3 & 0 bmatrix . Observe that A^T = -A , which implies that A is a skew-symmetric matrix. We need to compute A + 2A^T . Substituting A^T = -A into the expression, we get A + 2(-A) = A - 2A = -A . Since A^T = -A , it follows that -A = A^T . Therefore, A + 2A^T = A^T . Answer: A^T

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