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Consider the following two ordered bases of R³: B C P = C+B = = a. Find the change of basis matrix from the basis B3 to the basis C. {(0, 1, -1), (0, 0, 1), (-1,1,0)}, {(2, 1, 1), (−2, 0, −1), (−3, —1, −2)}.

Consider the following two ordered bases of R³: B C P = C+B = = a. Find the change of basis matrix from the basis B3 to the basis C. {(0, 1, -1), (0, 0, 1), (-1,1,0)}, {(2, 1, 1), (−2, 0, −1), (−3, —1, −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 the following two ordered bases of R³: P = C-B B с = a. Find the change of basis matrix from the basis B to the basis C. P = B-C = b. Find the change of basis matrix from the basis C to the basis B. {(0, 1, 1), (0, 0, 1), (−1, 1, 0) }, {(2, 1, 1), (-2, 0, −1), (−3, −1, −2)}. -
Transcribed Image Text:Consider the following two ordered bases of R³: P = C-B B с = a. Find the change of basis matrix from the basis B to the basis C. P = B-C = b. Find the change of basis matrix from the basis C to the basis B. {(0, 1, 1), (0, 0, 1), (−1, 1, 0) }, {(2, 1, 1), (-2, 0, −1), (−3, −1, −2)}. -
Consider the ordered bases B = ((3, –4), (1, −1)) and C = ((−4, −2), (−3,−4)) for the vector space R². a. Find the transition matrix from C to the standard ordered basis E = = ((1,0), (0, 1)). P E-C P = E-B b. Find the transition matrix from B to E. 1 P B-E -4 -2 P = B-C 3 -4 [v] B = c. Find the transition matrix from E to B. -1 4 -3 -4 6 -1 d. Find the transition matrix from C to B. 7 -22 -1 3 -24 e. Find the coordinates of u - (3,-1) in the ordered basis B. Note that [u] B = [u]E. B-E [u] B = f. Find the coordinates of u in the ordered basis B if the coordinate vector of v in C is [v]c = (1, 2).
Transcribed Image Text:Consider the ordered bases B = ((3, –4), (1, −1)) and C = ((−4, −2), (−3,−4)) for the vector space R². a. Find the transition matrix from C to the standard ordered basis E = = ((1,0), (0, 1)). P E-C P = E-B b. Find the transition matrix from B to E. 1 P B-E -4 -2 P = B-C 3 -4 [v] B = c. Find the transition matrix from E to B. -1 4 -3 -4 6 -1 d. Find the transition matrix from C to B. 7 -22 -1 3 -24 e. Find the coordinates of u - (3,-1) in the ordered basis B. Note that [u] B = [u]E. B-E [u] B = f. Find the coordinates of u in the ordered basis B if the coordinate vector of v in C is [v]c = (1, 2).
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