1 -5 11 Problem 3 Let W = Span(l%] , [_05} : [145]) 3 -5 19 w 2z + 2=0 (1) Let U be the set of solutions of the linear system 3w 4z+ y 5z2=0 w 6zx+ 3y+ 2z2=0 (a) Give a spanning set of W + U. hint: we know how to describe the sum of two \"Span(some vectors)\" so the first step is to get a Span description of both subspaces (b) Do we have R* = W 4 U? (c) Give a Cartesian equation and a spanning set of U N W. (2) Let V be the set of solutions of the linear equation w - 4x - 2y + 3z = 0. (a) Show that is in V. | WOHNH OT CIL (b) Show that 0 is in V. 5 11 (c) Show that 15 4 is in V. 19 (d) Conclude that W C V