3-1 Let P -3 -5 and v 3 Complete parts (a) and (b). 15 a. Find a basis (u, U, U) for R'such that P is the change-of-coordinates matrix from (u, u. u) to the basis (v, V2. V3) Hint: What do the columns of P represent?) b. Find a basis (W, W, w) for R' such that P is the change-of-coordinates matrix from (v. Va. V3) to (W. W2. Wa)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3 -1
-7
Let P=-3 -5
2 V2
and v3
3 Complete parts (a) and (b).
a. Find a basis (u,. uz. u3) for R' such that P is the change-of-coordinates matrix from (u. uz, ug) to the basis (v. V2. V3). Hint: What do the columns of P represent?)
b. Find a basis (w,. w, wa) for R' such that P is the change-af-coordinates matrix from (v,. v2. v) to (w,
Transcribed Image Text:3 -1 -7 Let P=-3 -5 2 V2 and v3 3 Complete parts (a) and (b). a. Find a basis (u,. uz. u3) for R' such that P is the change-of-coordinates matrix from (u. uz, ug) to the basis (v. V2. V3). Hint: What do the columns of P represent?) b. Find a basis (w,. w, wa) for R' such that P is the change-af-coordinates matrix from (v,. v2. v) to (w,
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