Let B Let v = x1 || 2 {]-G]} 3 13 15 then 8 0 be a basis for the subspace H. X1 where " x2 X2

(3) Let W be the subspace of R³ with orthogonal basis {u₁, u₂}, where 1 --0---0 = 1 -2 Let = -6 y = -3 1 2 Write y as the sum of a vector in W and a vector in W¹.

Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 7x - 2x² + 2, ·(x² + 2x +2) and 3x − x² + 1. 1 a. The dimension of the subspace H is b. Is {7x − 2x² +2,- (x² + 2x +2), 3x − x² +1} a basis for ➡? choose Be sure you can explain and justify your answer. c. A basis for the subspace His { Enter a polynomial or a comma separated list of polynomials (where you can enter xx in place of x²)

Let fi = 1+2x + 3x², f2 = 2 + 3x + 4x². B = (f1, f2) is a basis for the subspace V = {ao +a1x+azx²[ao – 2a1 +a2 = 0} of R2[r]. Let g = 1+5x + 9x². If [g]g = (,) then s = a) -7 b) -5 c) 5 d) 7 e) g is not in V.

Let W be the subspace spanned by -31 64 3 -3 2 5 2 3 Find an orthonormal basis for W.