Consider the following two ordered bases of R³:P =C-BBс=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)).PE-CP =E-Bb. Find the transition matrix from B to E.1PB-E-4-2P =B-C3-4[v] B =c. Find the transition matrix from E to B.-14-3-46-1d. Find the transition matrix from C to B.7-22-13-24e. 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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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)}.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 18CM

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Question

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).

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