Show that {u₁, u2} is an orthogonal basis for R². Then express x as a linear combination of the u's. 2 12 2 པཏཱ = Աշ = and x = 6 -2

Let u = (1,3, 5) and v = (-4,3, –7) be vectors in R3. (a) Find u + v. (b) Express u in terms of the standard basis vectors in R3. (c) Find -3u.

Find the coordinate vector (v)s relative to the basis S= {v ,,v,,v;} 21 for v = (2, 1, -2), if V, = (2, 2, -1) V2 = (-1, -2, 1) V3 = (1, -1, 1)

Let the basis B = {b1, b2} and basis C = {c1, c2} where vectors b1 = (7 -2). b2 = 2 -1 , c1 = 4 1  c2= 5 2 Find the change of coordinates matrix from B to C. (b) Find the change of coordinates matrix from C to B.

Let y 18 = = || -91 -3 and u 5 4 -2 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2 orthogonal to u. x₂ = ts ||