Theorem 3.6.3. If A E Matmxn and 0 = ER" then A.0=0Rm. Proof. 0=-(A 0)+A 0thm.3.2.5A (-0)+A (0) thm.3.2.5A (-0+ 0) = A.0. Definition 3.6.4. The kernel of a matrix A is the set ker(A) = {v |A. v=0}. Exercise 3.6.5. Using the same generality (i.e. abstractly, not using a particular matrix) as above, prove that if u and var both in the kernel of a matrix A, then Span{u, v} C ker(A). Does it change anything if I take 3 vectors? 4 vectors? k-man vectors? (See me if you want some help with abstract proofs.)