u = (+), V = = (44), W = 2 1 (³). For which values r R is the set {u, v, w} linearly independent?

Express w as a linear combination of u and v. 1 HHH] W = 5 u= 1 - 8 w=u+v (Type integers or fractions.) - 3

Let u=<-1,1> v=<-3,4> and w=<0,-2> Find u-v+4w

Let r E R and -- ), v= (), w= (!). 3 u = w = 2 For which values r ER is the set {u, v, w} linearly independent?

X b) Let T 10 Find the Kernel of T. Write down the range of T as a span of independent 5x vectors. What is the dimension of range of T?

Let A = {4, 5, 7} and B = {x, y}. Let p1 and p2 be the projections of A ✕ B onto the first and second coordinates. That is, for each pair (a, b)  A ✕ B, p1(a, b) = a and p2(a, b) = b. (a) Find p1(4, y) and p1(7, x) What is the range of p1? (Enter your answer in set-roster notation.) (b) Find p2(4, y) and p2(7, x). What is the range of p2? (Enter your answer in set-roster notation.)

Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

Let For what value of h is y in the plane spanned by v1 h 1 --·--· ·- V1 = 2 V2 = -3 y = = -2 and v₂? 5 14 h

Let u = (1, 2, 3), v = (4, 4, -2), and w = (6, -1, -2). Find z, where 2u + v − w + 3z = 0. - 0, -3, -2 Z = X

Let v (a) 20 = - (1, 4, 2) and w 4w = (b) Let s = t = = (1, - 4,0). (-2,24,4) (t, 1, 0). For which value(s) of t are w and 3 parallel?