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NDA2022MathematicsMatricesActual

Paragraph: Let A= ( array ccc 0 & ^2 & ^2 ^2 & 0 & ^2 ^2 & ^2 & 0 array ) and A=P+Q where P is symmetric matrix and Q is skew-symmetric matrix. Question: What is Q equal to ?

Options

  1. A( array ccc 0 & 1 / 2 & 1 / 2 1 / 2 & 0 & 1 / 2 1 / 2 & 1 / 2 & 0 array )
  2. B( array lll 0 & 1 & 1 1 & 0 & 1 1 & 1 & 0 array )
  3. C2 ( array ccc 0 & -1 & 1 1 & 0 & -1 -1 & 1 & 0 array )
  4. D2 ( array ccc 0 & -1 / 2 & 1 / 2 1 / 2 & 0 & -1 / 2 -1 / 2 & 1 / 2 & 0 array )

Correct answer

D. 2 ( array ccc 0 & -1 / 2 & 1 / 2 1 / 2 & 0 & -1 / 2 -1 / 2 & 1 / 2 & 0 array )

Step-by-step solution

aligned & Q= 1 2 (A-A^T )= 1 2 [ array ccc 0 & - 2 & 2 2 & 0 & - 2 - 2 & 2 & 0 array ] & = 2 [ array ccc 0 & -1 / 2 & 1 / 2 1 / 2 & 0 & -1 / 2 -1 / 2 & 1 / 2 & 0 array ] aligned

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