AP EAMCET20225 Jul 2022Morning ShiftMathematicsMatricesActual
If A= [ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] , then A A^T is a
Options
- Asymmetric matrix
- Bskew-symmetric matrix
- Csingular matrix
- Dinverse of A
Correct answer
A. symmetric matrix
Step-by-step solution
Here, aligned A & = [ array ccc 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] A^T & = [ array ccc 3 & 2 & 0 -3 & -3 & -1 4 & 4 & 1 array ] aligned aligned A A^T & = [ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] [ array ccc 3 & 2 & 0 -3 & -3 & -1 4 & 4 & 1 array ] A A^T & = [ array lll 9+9+16 & 6+9+16 & 0+3+4 6+9+16 & 4+9+16 & 0+3+4 0+3+4 & 0+3+4 & 0+1+1 array ] aligned aligned & A A^T= [ array lll 34 & 31 & 7 31 & 29 & 7 7 & 7 & 2 array ] & (A A^T )^T= [ array ccc 34 & 31 & 7 31 & 29 & 7 7 & 7 & 2 array ] aligned