MATH 235 Midterm: MATH 235 UMass Amherst uniform-practice-midterm
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Write yes if s is a subspace and no if s is not a subspace: (2 pts) No: s is not closed under scalar multiplication. Yes : s = ker(cid:0)(cid:2)1 1 1(cid:3)(cid:1). x y z. : x + y + z = 0 . S is the set of vectors of the form c. 0 a + 2b + 3c: (2 pts) Yes : s = im : (2 pts) S is the set polynomials p in p3 such that p (2) = 0. Yes : s = ker(t ), where t : p3 p3 is the linear transformation t (p) = p (2): (10 points) solve the following system of linear equations. For t r. t: (10 points) solve the following system of linear equations. x z = 1 x + 2y + 3z = 11. The solutions are x = 1 + t, y = 5 2t, z = t for t r.
