True or false questions on subspaces?

please help me





true or false for M = all 3 by 3 matrices (check addition using an example)?





a) the skew symmetric matrices in M (with A Transpose= -A) form a subspace





b) the unsymmetric matrices in M ( with A transpose not equal to A ) form a subspace





c) the matrices that have (1,1,1) in their nullspace form a subspace.





thanks so much. True or false questions on subspaces?
a) true. let k,l be arbitrary numbers and A B two skew symmetric matrices, then


(kA + lB)^t = kA^t + lB^t = -kA - lB = -(kA+lB)


by the property of transpose.





b) false. Let A be an unsymmetric matrix. Then A^t =/= A, so that A^t is also an unsymmetric matrix. But A+A^t is symmetric.





c) true. If A and B have a particular vector v in their subspace, this means





Av = Bv = 0





Then





(kA+lB)v = (kAv+lBv) = k(0) + l(0) = 0