Let A=3a-125cb82 is symmetric and B=d3ab-ae-2b-c-26-f is skew-symmetric, find AB.

# Let $A=\left[\begin{array}{ccc}3& a& -1\\ 2& 5& c\\ b& 8& 2\end{array}\right]$ is symmetric and $B=\left[\begin{array}{ccc}d& 3& a\\ b-a& e& -2b-c\\ -2& 6& -f\end{array}\right]$ is skew-symmetric, find $AB$.

1. A

$AB=\left[\begin{array}{ccc}4& -3& 6\\ -31& 54& -26\\ -28& 9& -50\end{array}\right]$

2. B

$AB=\left[\begin{array}{ccc}-4& 3& -6\\ -31& 54& -26\\ -28& 9& -50\end{array}\right]$

3. C

$AB=\left[\begin{array}{ccc}4& 3& -6\\ 31& 54& 26\\ -28& 9& -50\end{array}\right]$

4. D

$AB=\left[\begin{array}{ccc}4& 3& 6\\ 31& -54& 26\\ -28& 9& -50\end{array}\right]$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

is symmetric

is skew-symmetric       ..(i)

..(ii)

From Eqs. (i) and (ii), we get

and $B=\left[\begin{array}{ccc}0& 3& 2\\ -3& 0& -6\\ -2& 6& 0\end{array}\right]$  +91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)