please answer d,e,f and g. Thank you! Q 6Discuss 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 = Id) Let A be an m x m real matrix. If A is skew-symmetric and m is odd, then A isnonsingular.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 Rf) If the columns of A are linearly independent then AAT is always nonsingular.

Name: please answer d,e,f and g. Thank you! Q 6Discuss whether the following
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Description: please answer d,e,f and g. Thank you! Q 6Discuss 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

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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.