If a is A symmetric matrix and B is a skew-symmetrix matrix such that A + B = [2&3 5&-1] , then AB is equal to :

Question

If a is A symmetric matrix and B is a skew-symmetrix matrix such that A + B = [2&3 5&-1] , then AB is equal to : (A) [ -4&2 1&4] (B) [ -4& -2 - 1&4] (C) [ 4& -2 -1&-4] (D) [ 4 -2 1 -4]

Tardigrade Admin · Accepted Answer

A = A' , B = - B' A + B = [2&3 5&-1] ....(1) A' + B' = [2&5 3 &-1] A -B = [2&5 3&-1] .....(2) After adding Eq. (1) (2) A = [2&4 4 &-1] , B = [0&-1 1 &0] AB = [4&-2 -1 &-4]

Q. If a is $A$ symmetric matrix and $B$ is a skew-symmetrix matrix such that $A + B = [25 3 - 1]$ , then AB is equal to :

$[- 4 1 24]$

$[- 4 - 1 - 2 4]$

$[4 - 1 - 2 - 4]$

$[41 - 2 - 4]$

$A = A^{'}, B = - B^{'}$
$A + B = [25 3 - 1]$ ....(1)
$A^{'} + B^{'} = [23 5 - 1]$
$A - B = [23 5 - 1]$ .....(2)
After adding Eq. (1) & (2)
$A = [24 4 - 1], B = [01 - 1 0]$
$A B = [4 - 1 - 2 - 4]$

Q. If a is A symmetric matrix and B is a skew-symmetrix matrix such that A+B=[25​3−1​], then AB is equal to :

[−41​24​]

[−4−1​−24​]

[4−1​−2−4​]

[41​−2−4​]