Math 103 Homework 4.2 Name: -3 1) Let A = 6 W - 0 determine if w = is in Nul A. 2) Find an explicit description of Nul A by listing vectors that span the null space. 16 1 4 0 3) Find an explicit description of Nul A by listing vectors that span the null space. -2 0 4 10 1 -9 0 0 0 4) Determine if the following set of vectors is a vector space. To prove "yes", use an appropriate theorem, to prove "no", show a counterexample. a) W : a + b + c = 2, a, b, c real b ) W a - 2b = 40. a, `2a = c + 3dia, b c, d real[b - 2d] c) W = 5 + d b + 3d :b, d real 5. Find the matrix A such that the given set is Col A. 2s + 3t r +s - 2t 4r + s :T,s treal 3r - s - -6 6. Given A = w ! 12 a) The nul A is a subspace of Ri, what is j? b) The col A is a subspace of RK, what is k? c) Find a non-zero vector in Nul A d) Find a non-zero vector in Col A. 7. Let A = 6 8 8 anaw - [; ]. a) Determine if W is in Col A? Show your work. b) determine if W is in Nul A? Show your work. 6 -4 8. Let A = 0 9 -11 and w - 19 -9 7 a) Determine if W is in Col A? Show your work. b) determine if W is in Nul A? Show your work