A real matrix A is skew symmetric if A' = -A. (a) Show that a (2n+1)x(2n+1)...

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A real matrix A is skew symmetric if A' = -A. (a) Show that a (2n+1)x(2n+1) skew symmetric matrix has a non-trivial null-space. (b) Show that if A is an eigenvalue of A, then so is -2. (c) Show that the spectrum of A is purely imaginary, i.e., consists of num- bers of the form {i1;} where the 2; e R. (d) Show that det A > 0. A real matrix A is skew symmetric if A' = -A. (a) Show that a (2n+1)x(2n+1) skew symmetric matrix has a non-trivial null-space. (b) Show that if A is an eigenvalue of A, then so is -2. (c) Show that the spectrum of A is purely imaginary, i.e., consists of num- bers of the form {i1;} where the 2; e R. (d) Show that det A > 0.