2. Determine if the set is a basis of R3 [t] . {t² + 2t -3, t² + 5t, 2t² — 4}

Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x²} O sis linearly dependent. s does not span P2. S is linearly dependent and does not span P,.

The set B = {1– 2t + t²,3 – 5t + 4t2 , 2t + 3t²} is a basis of P2. Suppose C = {c1, c2, C3} is another basis of P2 such 4 11 that P = C+B Determine the polynomials c1(t), c2(t), and c3(t). 1 3 -1

Find a basis for P2 containing the linearly independent set {8x2-3x+7}