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 P equal to?
Options
- A( array ccc 0 & 1 / 2 & 1 / 2 1 / 2 & 0 & 1 / 2 1 / 2 & 1 / 2 & 0 array )
- B( array lll 0 & 1 & 1 1 & 0 & 1 1 & 1 & 0 array )
- C2 ( array ccc 0 & -1 & 1 1 & 0 & -1 -1 & 1 & 0 array )
- D2 ( array ccc 0 & -1 / 2 & 1 / 2 1 / 2 & 0 & -1 / 2 -1 / 2 & 1 / 2 & 0 array )
Correct answer
A. ( array ccc 0 & 1 / 2 & 1 / 2 1 / 2 & 0 & 1 / 2 1 / 2 & 1 / 2 & 0 array )
Step-by-step solution
aligned & A= [ array ccc 0 & ^2 & ^2 ^2 & 0 & ^2 ^2 & ^2 & 0 array ] & A^T= [ array ccc 0 & ^2 & ^2 ^2 & 0 & ^2 ^2 & ^2 & 0 array ] & P= 1 2 (A+A^T )= [ array ccc 0 & 1 / 2 & 1 / 2 1 / 2 & 0 & 1 / 2 1 / 2 & 1 / 2 & 0 array ] aligned