Which function is a linear function? 1 - 3x2 = - y y + 7 = 5x x3 + 4 = y 9 (x2 - y) = 3 y - x3 = 8

Let δ = {1, x, x 2} be the standard basis for P2 and consider the linear transformation T : P2 → R 3 defined by T (f) = [f]δ, where [f]δ is the coordinate vector of f with respect to δ. Now, β is a basis for P2 if and only if T (β) =      1 1 0  ,   1 0 1  ,   0 1 1      is a basis for R 3. (This follows from Theorem 8 on page 244. For further explanation, see Exercises 25 and 26 on page 249.) To check T (β) is a basis for R 3, it suffices to put the three columns in 3 * 3 matrix and show that the rref of this matrix is the identity matrix. (This computation is trivial, so I won’t reproduce it here!)