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Consider B = the standard basis for IR, and B' = another basis for R. For these bases: Part (a): Construct a transition matrix from B to B' and from B' to B. Clearly label which is which. Part (b): Given the vector [u]g -1 (in the standard basis), use the result of part (a) to write [ug. 1 Part (c): Given the vector [vg' 2 (in the B' basis), use the result of part (a) to write [v]g. -2

Consider B = the standard basis for IR, and B' = another basis for R. For these bases: Part (a): Construct a transition matrix from B to B' and from B' to B. Clearly label which is which. Part (b): Given the vector [u]g -1 (in the standard basis), use the result of part (a) to write [ug. 1 Part (c): Given the vector [vg' 2 (in the B' basis), use the result of part (a) to write [v]g. -2

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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Consider B = , the standard basis for R, and B' = another basis for R. For these bases: Part (a): Construct a transition matrix from B to B' and from B' to B. Clearly label which is which. Part (b): Given the vector [u]g -1 (in the standard basis), use the result of part (a) to write uR'. 3 Part (c): Given the vector vg' (in the B' basis), use the result of part (a) to write [v]R.
Transcribed Image Text:Consider B = , the standard basis for R, and B' = another basis for R. For these bases: Part (a): Construct a transition matrix from B to B' and from B' to B. Clearly label which is which. Part (b): Given the vector [u]g -1 (in the standard basis), use the result of part (a) to write uR'. 3 Part (c): Given the vector vg' (in the B' basis), use the result of part (a) to write [v]R.
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