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(i) Find the change-of-basis matrix Ps,-E and then use it to find the component vector [C]s, of - with respect to S1. (ii) Find the change-of-basis matrix Ps,t-E and then use it to find the component vector [C]s, with respect to S2. (iii) Find the change-of-basis matrix Ps,t-S1. Check your work by computing [C]s, Pszt-Sı [C]s{ •

(i) Find the change-of-basis matrix Ps,-E and then use it to find the component vector [C]s, of - with respect to S1. (ii) Find the change-of-basis matrix Ps,t-E and then use it to find the component vector [C]s, with respect to S2. (iii) Find the change-of-basis matrix Ps,t-S1. Check your work by computing [C]s, Pszt-Sı [C]s{ •

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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(i) Find the change-of-basis matrix Ps,+E and then use it to find the component vector [C]s, of 4 C = -1 with respect to S1. (ii) Find the change-of-basis matrix Ps,-E and then use it to find the component vector [C]s, with respect to S2. (iii) Find the change-of-basis matrix Ps,-S1. Check your work by computing [C]s, Psz-S1[C]sq•
Transcribed Image Text:(i) Find the change-of-basis matrix Ps,+E and then use it to find the component vector [C]s, of 4 C = -1 with respect to S1. (ii) Find the change-of-basis matrix Ps,-E and then use it to find the component vector [C]s, with respect to S2. (iii) Find the change-of-basis matrix Ps,-S1. Check your work by computing [C]s, Psz-S1[C]sq•
5. Let V be the vector space of 2 x 2 upper-triangular matrices. Three ordered bases for V are 2 1 0 2 1 0 1 1 2 1 3 S1 S2 -1 0 1 0 0 0 2 0 1 and {b 0 1 1 0 0 0 E 0 0 0 1
Transcribed Image Text:5. Let V be the vector space of 2 x 2 upper-triangular matrices. Three ordered bases for V are 2 1 0 2 1 0 1 1 2 1 3 S1 S2 -1 0 1 0 0 0 2 0 1 and {b 0 1 1 0 0 0 E 0 0 0 1
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