Consider the following two ordered bases of R³: {(1, 1, 1), (–1,0, –-1), (3, 1, 2)}, {(2, 1, –1), (2, 2, –-1), (3, 2, –1)}. В a. Find the change of basis matrix from the basis B to the basis C. [id; = |-2 1 -1 -2 5 7 [ 3 3 4 b. Find the change of basis matrix from the basis C to the basis B. [id = -3 2 -5 -1 2 -6 3 -3 7
Consider the following two ordered bases of R³: {(1, 1, 1), (–1,0, –-1), (3, 1, 2)}, {(2, 1, –1), (2, 2, –-1), (3, 2, –1)}. В a. Find the change of basis matrix from the basis B to the basis C. [id; = |-2 1 -1 -2 5 7 [ 3 3 4 b. Find the change of basis matrix from the basis C to the basis B. [id = -3 2 -5 -1 2 -6 3 -3 7
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 69E: Find a basis for R2 that includes the vector (2,2).
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3.2 Question 8
![Consider the following two ordered bases of R3:
B
{(1, 1, 1), (–1,0, –1), (3, 1, 2)},
с %3D {(2,1, —1), (2, 2, —1), (3, 2, -1}}.
a. Find the change of basis matrix from the basis B to the basis C.
[id
[-2
1
-1
-2
5
6.
7
[ 3
3
4
b. Find the change of basis matrix from the basis C to the basis B.
[id]%
[ -3
-5
-1
2
-6
[ 3
-3
7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F326a7328-130e-4258-98d9-f22d8fa27a9c%2F89ca790e-8c97-4478-bd57-2c84e364f58c%2Fic70ir_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following two ordered bases of R3:
B
{(1, 1, 1), (–1,0, –1), (3, 1, 2)},
с %3D {(2,1, —1), (2, 2, —1), (3, 2, -1}}.
a. Find the change of basis matrix from the basis B to the basis C.
[id
[-2
1
-1
-2
5
6.
7
[ 3
3
4
b. Find the change of basis matrix from the basis C to the basis B.
[id]%
[ -3
-5
-1
2
-6
[ 3
-3
7
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