Determinants Matrices Question 118
Question: If A is a square matrix, then $ AA^{T} $ is a
Options:
A) Skew-symmetric matrix
B) Symmetric matrix
C) Diagonal matrix
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] Let $ A= \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & 0 \\ 1 & -1 & 2 \\ \end{bmatrix} , $ then $ A’= \begin{bmatrix} 1 & 2 & 1 \\ -1 & 1 & -1 \\ 1 & 0 & 2 \\ \end{bmatrix} $
$ \therefore AA’= \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & 0 \\ 1 & -1 & 2 \\ \end{bmatrix} \begin{bmatrix} 1 & 2 & 1 \\ -1 & 1 & -1 \\ 1 & 0 & 2 \\ \end{bmatrix} = \begin{bmatrix} 3 & 1 & 4 \\ 1 & 5 & 1 \\ 4 & 1 & 4 \\ \end{bmatrix} $
BETA
