Define two ordered bases В - and E = on R³. (i) Find the vector v1 of R³ whose component vector with respect to B is [v1]B = and write its component vector [V1]E with respect to E. (ii) Find the 3 × 3 change-of-basis matrix PE-B. Check your answer by computing [vi]E = Pet-B[V1]B;, and comparing to what you found in part (i).
Define two ordered bases В - and E = on R³. (i) Find the vector v1 of R³ whose component vector with respect to B is [v1]B = and write its component vector [V1]E with respect to E. (ii) Find the 3 × 3 change-of-basis matrix PE-B. Check your answer by computing [vi]E = Pet-B[V1]B;, and comparing to what you found in part (i).
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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![- Define two ordered bases
B =
and
E =
on R³.
-1
(i) Find the vector v1 of R³ whose component vector with respect to B is [v1]B
-3
and write its component vector [v1]E with respect to E.
(ii) Find the 3 × 3 change-of-basis matrix PE-B. Check your answer by computing
[vi]E = PE-B[Vi]B,
and comparing to what you found in part (i).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67429e19-8d15-47bc-bbfe-dfa923849540%2F4569ca9e-ed6e-4a6e-9989-477cf544dde2%2F2pai25h_processed.png&w=3840&q=75)
Transcribed Image Text:- Define two ordered bases
B =
and
E =
on R³.
-1
(i) Find the vector v1 of R³ whose component vector with respect to B is [v1]B
-3
and write its component vector [v1]E with respect to E.
(ii) Find the 3 × 3 change-of-basis matrix PE-B. Check your answer by computing
[vi]E = PE-B[Vi]B,
and comparing to what you found in part (i).
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