d) Let A be an m x m real matrix. If A is skew-symmetric and m is odd, then A is nonsingular. e) The dimension of the vector space of 4 x 4 real symmetric matrices is 10. e) The hyperplane r + 2y+ 3z = 5 is a vector subspace of R3 f) If the columns of A are linearly independent then AAT is always nonsingular.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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please answer d,e,f and g. Thank you!

Q 6
Discuss whether the following statements are True or False. Justify your answer.
a) A projection matrix P has a single nonzero eigenvalue which is 1.
b) For a complex matrix A, determinant of A and A" is always the same.
c) If A is Hermitian and Unitary then A2 = I
d) Let A be an m x m real matrix. If A is skew-symmetric and m is odd, then A is
nonsingular.
e) The dimension of the vector space of 4 x 4 real symmetric matrices is 10.
e) The hyperplane r+ 2y + 3z = 5 is a vector subspace of R
f) If the columns of A are linearly independent then AAT is always nonsingular.
Transcribed Image Text:Q 6 Discuss whether the following statements are True or False. Justify your answer. a) A projection matrix P has a single nonzero eigenvalue which is 1. b) For a complex matrix A, determinant of A and A" is always the same. c) If A is Hermitian and Unitary then A2 = I d) Let A be an m x m real matrix. If A is skew-symmetric and m is odd, then A is nonsingular. e) The dimension of the vector space of 4 x 4 real symmetric matrices is 10. e) The hyperplane r+ 2y + 3z = 5 is a vector subspace of R f) If the columns of A are linearly independent then AAT is always nonsingular.
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