Number 10 from 5.4 22. If A is diagonalizable ancdiagonalizable.9. Define T : P2 → R³ by T(p) =p(0)P(1)a. Find the image under T of p(t) = 5+ 3t.23. If B = P-'AP and x is ato an eigenvalue 1, then Fsponding also to 2.b. Show that T is a linear transformation.c. Find the matrix for T relative to the basis {1,t,t2} for P2and the standard basis for R3.24. If A andB are similar, theRefer to Supplementary E-P(-2)p(3)p(1)p(0)a. Show that T is a linear transformation.25. The trace of a square ma10. Define T : P3 → R* by T(p) =entries in A and is denotetr(FG) = tr(GF) for an-Show that if A and B are sb. Find the matrix for T relative to the basis {1, t,t²,t³} forP3 and the standard basis for R*.26. It can be shown that the trathe eigenvalues of A. VerifA is diagonalizable.In Exercises 11 and 12, find the B-matrix for the transformationXH Ax, where B = {b¡,b2}.27. Let V be R" with a basiswith the standard basis, deidentity transformation Ithe matrix for I relative t-411. A =6.-1b2 =called in Section 4.4?-612. A =4b, =b, =28. Let V be a vector space wbe the same space V withIn Exercises 13–16, define T : R² → R² by T(x) = Ax. Find abasis B for R? with the property that [T]B is diagonal.be the identity transformafor I relative to B and CSection 4.7?13. А 314. A =-329. Let V be a vector space Ethe B-matrix for the iden-215. A =16. A =[M] In Exercises 30 and 31, fition x > Ax where B = {b1,17. Let A =and B = {b1, b2}, for b¡ =6 -2 -21 -230. A =b2 =Define T: R2 → R² by T(x) = Ax.2 -2217, b2 =| 1[27a. Verify that bị is an eigenvector of A but that A is notdiagonalizable.bj =b. Find the B-matrix for T.13-7 -48 -166.18. Define T: R³ → R³ by T (x)matrix with eigenvalues 5, 5, and -2. Does there exist a basisB for R3 such that the B-matrix for T is a diagonal matrix?Discuss.= Ax, where A is a 3 x 331. A=114-3 -45 -19-3b =1,b2 DVerify the statements in Exercises 19-24. The matrices are square.-319. If A is invertible and similar to B, then B is invertibleand A- is similar to B-. [Hint: P-AP = B for someinvertible P. Explain why B is invertible. Then find aninvertible Q such that 0-A-0 = R-132. [M] Let T be the transfgiven below. Find a basisis diagonal.

Name: Number 10 from 5.4 22. If A is diagonalizable ancdiagonalizable.9. Def
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Description: Number 10 from 5.4 22. If A is diagonalizable ancdiagonalizable.9. Define T : P2 → R³ by T(p) =p(0)P(1)a. Find the image under T of p(t) = 5+ 3t.23. If B = P-'AP and x is ato an eigenvalue 1, then Fsponding also to 2.b. Show that T is a linear transf