Number 30 is {1, t, t2,t} forthe eigenvalues of A. Verify this statement for the case whenA is diagonalizable.e transformation27. Let V be R" with a basis B = {b1, ..., b,}; let W be R"with the standard basis, denoted here by ɛ; and consider theidentity transformation I : R" → R", where I(x) = x. Findthe matrix for I relative to B and E. What was this matrixcalled in Section 4.4?28. Let V be a vector space with a basis B = {b,..., b,}, let Wbe the same space V with a basis C = {c...., c,}, and let Ibe the identity transformation I : V → W. Find the matrixfor I relative to B and C. What was this matrix called inSection 4.7?= Ax. Find anal.29. Let V be a vector space with a basis B = {bj,..., b,}. Findthe B-matrix for the identity transformation I: V →V.[M] In Exercises 30 and 31, find the B-matrix for the transforma-tion x→ Ax where B = {b1, b2, b3}.b1 =Г6 -2 -230. А — | 3 1 -2 |,|2 -2Ax.hat A is notb1 =1, b2 =1, b3 =3is a 3 x 3-7 -48 -1631. A =1146.exist a basisnal matrix?-3 -45 -19-3-21, b2 =b1 =-3b3are square.= invertible3 for some32. [M] LetT be the transformation whose standard matrix isgiven below. Find a basis for R with the property that [ T ]Ris diagonal.en find an-69.-3A =-1 -21is similar-440.4.

Name: Number 30 is {1, t, t2,t} forthe eigenvalues of A. Verify this stateme
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Description: Number 30 is {1, t, t2,t} forthe eigenvalues of A. Verify this statement for the case whenA is diagonalizable.e transformation27. Let V be R" with a basis B = {b1, ..., b,}; let W be R"with the standard basis, denoted here by ɛ; and consider theident