Need help with d e and f d) Consider the linear map T : C → C³ whose matrix in the standard basis e1, e2, e3is(0 10 0 10 0 0For a, b, c € C, defineB2 = aez,Show that these 31, 32, Ba is a basis of C if and only if both a and c are # 0.B = e1,B3 = bez + cae3.1For a and c both + 0, find the matrix of T in the base B1, B2, B3.0 1 0similar to (0 0 10 0 0(1 1 00 1 10 0 1(0 a be) For which a, b, c€ C is the matrix (0 0 c0 0 01a bf) For which a, b, c € C is the matrix (0 10 0 1similar to

d) Consider the linear map T: C→ C whose matrix in the standard basis e1, e2, e3 is (0 1 0V 0 0 1 0 0 0 For a, b,c € C, define B = e1, B = aez, B = bez + cae3. Show that these B, B2, Ba is a basis of C if and only if both a and c are #0. 1 For a and c both # 0, find the matrix of T in the base B, B2, Bs. 0 1 0 similar to 0 0 1 0 0 0 1 1 0 similar to (0 1 (0 a b e) For which a, b, c e C is the matrix (00 c 0 00 1ab f) For which a, b, c e C is the matrix (0 1 c 0 0 1 00 1

d) Consider the linear map T: C→ C whose matrix in the standard basis e1, e2, e3 is (0 1 0V 0 0 1 0 0 0 For a, b,c € C, define B = e1, B = aez, B = bez + cae3. Show that these B, B2, Ba is a basis of C if and only if both a and c are #0. 1 For a and c both # 0, find the matrix of T in the base B, B2, Bs. 0 1 0 similar to 0 0 1 0 0 0 1 1 0 similar to (0 1 (0 a b e) For which a, b, c e C is the matrix (00 c 0 00 1ab f) For which a, b, c e C is the matrix (0 1 c 0 0 1 00 1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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