Let V = P² be the vector space of polynomials of degree at most 2, and let B be the basis {f1, f2, f3}, where fi (t) = t? – 2t + 1 and f2(t) = 242 – t – 1 and f3(t) = t. Find the coordinate vector [t² – 2]B (which expresses t² – 2 in terms of the chosen basis vectors).

Compute the scalar triple product u ( x w) of the vectors u = (0, 7, — 6), = (-8,0, – 3), and = (3, — 8, 9). ū · (v × w) .

The vector x is in a subspace H with a basis B = {b₁,b₂}. Find the B-coordinate vector of x. 5 1 = -LHCHO b2 -7 3 [X]B b₁ = = X= 5

a b 6. Let H be a subspace of M2x2 whose vectors are of the form Then, B с 0 is a basis for H. 10 Find the coordinate vector of v = according to the basis, B.