Question: Determine whether the linear transformation T is invertible by considering its matrix with respect to the standard bases. If T is invertible, use Theorem 6.28

Determine whether the linear transformation T is invertible by considering its matrix with respect to the standard bases. If T is invertible, use Theorem 6.28 and the method of Example 6.82 to find T^-1.

T in Exercise 5

Data From Exercise 5

T : P₂ †’ R² defined by T(P(x) ) [p(0)° Lp(1)] ||

B = {1, x, x²}, C = {e₁, e₂},

v = p(x) = a + bx + cx²

[p(0) Lp(1)] ||

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