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Consider the ordered bases B = ((1, 2), (-1,-1)) and C = ((-3, 1), (3, 1)) fo a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, = b. Find the transition matrix from B to E.

Consider the ordered bases B = ((1, 2), (-1,-1)) and C = ((-3, 1), (3, 1)) fo a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, = b. Find the transition matrix from B to E.

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 ordered bases B = ((1, 2), (-1, -1)) and C= ((-3, 1), (3, 1)) for the vector space R². a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). b. Find the transition matrix from B to E. TR = c. Find the transition matrix from E to B. 3 d. Find the transition matrix from C to B. TB = TB = e. Find the coordinates of u = (-1, -3) in the ordered basis B. Note that [u]B = T[u]E. [u] B f. Find the coordinates of u in the ordered basis B if the coordinate vector of u in C is [v]c = (1,1). [v]B=
Transcribed Image Text:Consider the ordered bases B = ((1, 2), (-1, -1)) and C= ((-3, 1), (3, 1)) for the vector space R². a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). b. Find the transition matrix from B to E. TR = c. Find the transition matrix from E to B. 3 d. Find the transition matrix from C to B. TB = TB = e. Find the coordinates of u = (-1, -3) in the ordered basis B. Note that [u]B = T[u]E. [u] B f. Find the coordinates of u in the ordered basis B if the coordinate vector of u in C is [v]c = (1,1). [v]B=
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