(Solved): 4. Recall that an nxn (a) How many parameters are needed to describe the set of 3 x 3 skew-symmetri ...

4. Recall that an nxn (a) How many parameters are needed to describe the set of 3 x 3 skew-symmetric matrices? (b) Show that if A is skew-symmetric, then Ax and x are orthogonal for all x ER". 5. Explain why the set V = {x € R131 +32 - 373 2 0} fails to be a subspace. 6. Give C(A), N(A), R(A) and N(AT) each as the span of a set of vectors. Use the fewest vectors possible. 1 1 1 1 2 0 A= 1 1 1 1 0 2 For example, the statement C(A) = Span((1,1,1,1),(1,2,1,0), (1,0,1,2)) is true but not the right answer because you could achieve the same result with fewer vectors.