Can you plz help me in solving this question?

Multiple options can be correct.

Screenshot

1 Answer
Apr 16, 2018

Answer:

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.