Can I have some help with this

3. {a} {2 points} State the denition of a subspace. {I-[intz this should contain 3 main parts...) [h] {3 points} Use the denition of a subspace to prove that if V is a subspace of IR" and if A is an m matrix? then AUX] is also a subspace of IR\". {Here 210'} denotes the set of all vectors of the form A where E is a vector inside V.) {c} {3 points} Find a matrix A such that the kernel of A is spanned by the vector (L2, ll}. [[1] {2 points} True or false? If true? prove why; if false, give a counterexample: [l' A and B are two um matrices with ker{A}I = rej and im[A} = m{B]I, then A and B are the same matrix