Can you plz help me in solving this question?

Multiple options can be correct.

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1 Answer
Apr 16, 2018

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.