devarshi-dt-logo

Question:

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

[?, ?, ?]

[?]

[?, ?, ?]

[?, ?, ?]

Solution:

A = A', B = -B'
A + B = [[2, 3, 5], [?, ?]] (1)
A' + B' = [[2, ?, ?], [3, 5, ?]]
A - B = [[2, ?, ?], [3, 5, ?]] (2)
Adding Eq (1) and (2):
2A = [[4, ?, ?], [?, ?, ?]]
A = [[2, ?, ?], [?, ?, ?]]
B = [[0, ?, ?], [?, ?, ?]]
AB = [[?, ?, ?]]