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Consider the ordered bases B = ((5, 4), (6, 5)) and C = ((-2,0), (0, -4)) for the vector space R?. a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). -2 P E-C -4 b. Find the transition matrix from B to E. P = E-B 4 c. Find the transition matrix from E to B. P = d. Find the transition matrix from C to B. P e. Find the coordinates of u = (-3,-3) in the ordered basis B. Note that [u]B = [ u]E. [u]B = f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]c = (1, 2). [v]B =

Consider the ordered bases B = ((5, 4), (6, 5)) and C = ((-2,0), (0, -4)) for the vector space R?. a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). -2 P E-C -4 b. Find the transition matrix from B to E. P = E-B 4 c. Find the transition matrix from E to B. P = d. Find the transition matrix from C to B. P e. Find the coordinates of u = (-3,-3) in the ordered basis B. Note that [u]B = [ u]E. [u]B = f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]c = (1, 2). [v]B =

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.4: Transistion Matrices And Similarity
Problem 15E
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Consider the ordered bases B = ((5,4), (6, 5)) and C = ((-2,0), (0, –4)) for the vector space R?. a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). -2 P E-C -4 b. Find the transition matrix from B to E. 6. P E-B 5 c. Find the transition matrix from E to B. P B-E d. Find the transition matrix from C to B. P B+C e. Find the coordinates of u = (-3, –3) in the ordered basis B. Note that [u]B = [ u]E: BE [u]B R = f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is (v]c = (1,2). [v]B = ||
Transcribed Image Text:Consider the ordered bases B = ((5,4), (6, 5)) and C = ((-2,0), (0, –4)) for the vector space R?. a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). -2 P E-C -4 b. Find the transition matrix from B to E. 6. P E-B 5 c. Find the transition matrix from E to B. P B-E d. Find the transition matrix from C to B. P B+C e. Find the coordinates of u = (-3, –3) in the ordered basis B. Note that [u]B = [ u]E: BE [u]B R = f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is (v]c = (1,2). [v]B = ||
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