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Let B = {A1, A2, A3, A4} and B2 = {C1, C2. Cs, C4} when : %3D %3D A3 A4 = 0 0 C; - (; }).c- (? :).c- (: ?).c - (" ?)- C4 = 1. Prove that B, and B2 are two basis of M2 (R). 2. Find the coordinates of D ) in the basis B. 5 3 3. Give the transition matrix Ps,-B,- 4. Using 3. deduce the coordinates of D in the basis By.

Let B = {A1, A2, A3, A4} and B2 = {C1, C2. Cs, C4} when : %3D %3D A3 A4 = 0 0 C; - (; }).c- (? :).c- (: ?).c - (" ?)- C4 = 1. Prove that B, and B2 are two basis of M2 (R). 2. Find the coordinates of D ) in the basis B. 5 3 3. Give the transition matrix Ps,-B,- 4. Using 3. deduce the coordinates of D in the basis By.

Advanced Engineering Mathematics
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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Let B1 = {A1, A2, A3, A4} and B2 = {C1, C2. C3, C4} when : %3D A = G 0). 4 = 6 = (; }),cs- (? !),cs- (::)«-(:?). 1 0 0 C2 C3 C4 = 1. Prove that B, and B2 are two basis of M2 (R). 6 2 2. Find the coordinates of D ( ) in the basis B1. 5 3 3. Give the transition matrix Ps,--B,. 4. Using 3. deduce the coordinates of D in the basis B.
Transcribed Image Text:Let B1 = {A1, A2, A3, A4} and B2 = {C1, C2. C3, C4} when : %3D A = G 0). 4 = 6 = (; }),cs- (? !),cs- (::)«-(:?). 1 0 0 C2 C3 C4 = 1. Prove that B, and B2 are two basis of M2 (R). 6 2 2. Find the coordinates of D ( ) in the basis B1. 5 3 3. Give the transition matrix Ps,--B,. 4. Using 3. deduce the coordinates of D in the basis B.
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