Decide which of the matrices A in Exercises 1 through 20 are diagonalizable. If possible, find an invertible S and a diagonal D such that S~lAS = D. Do not use technology.

L22 - 4 Notes on Error (if time): The error in using L(x)t opie f(x)svny |L(x) − f(x)|. In our example, we see that |L(x) − f(x)|≤ .000025 if |x − 2|≤ 0.04. The following theorem (page 211 in text) allows us to ﬁnd an upper bound for that error in general: Let f(x)beafncnw hescnddravextsnan interval (1 ,x2)ndheianumbr K so that ▯▯ |f (x)|≤ K for all x in the interval. If L(ielaiinf f(x) for some a in the interval (1 ,x2), then 1 |f(x) − L(x)|≤ K(x − a) 2 2 for all x in (1 ,2 ).