Question

Can you plz help me in solving this question?

Multiple options can be correct.

Answer 1

See below.

Explanation:

If `Y` is skew-symmetric then `Y = -Y^top`
If `Z` is symmetric then `Z = Z^top`

a)

`-(Y^3Z^4-Z^4Y^3)^top =-(Z^4(Y^top)^3-(Y^top)^3Z^4) = Z^4Y^3-Y^3Z^4 = -(Y^3Z^4-Z^4Y^3)` hence a) is a symmetric matrix.

b)

`X^44+Y^44 = (-X cdot X^top)^22 + (-Y cdot Y)^22` which is a symmetric matrix.

c)

`X^4Z^3-Z^3 X^4 = (-X X^top)^2 Z^3-Z^3 (-X X^dot)^2 = (X X^top)^2 Z^3-Z^3 (X X^top)^2 = -((X X^top)^2 Z^3-Z^3 (X X^top)^2)^top` hence this is a skew-symmetric matrix

d)

`X^23+Y^23 = (-X^top)^23 + (-Y^top)^23 = -(X^top)^23-(Y^top)^23 = -(X^23+Y^23)^top` hence d) is skew-symmetric.