Let B and C be bases for 2. If B and the change-of-basis matrix from B to C is find C

Chapter 6, Problem 6.3.16

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Let B and C be bases for 2. If B and the change-of-basis matrix from B to C is find C. PCdB 100 021 111 1 In calculus, you learn that a Taylor polynomial of degree nabout a is a polynomial of the formwhere an 0. In other words, it is a polynomial that hasbeen expanded in terms of powers of x a instead of powersof x. Taylor polynomials are very useful for approximatingfunctions that are well behaved near x a.The set is a basis forn for any real number a. (Do you see a quick way to showthis? Try using Theorem 6.7.) This fact allows us to use thetechniques of this section to rewrite a polynomial as a Taylorpolynomial about a given a.