Given basis C, and the change of basis matrix P, determine the basis B. (Hint: what does each column of _P_ represent?)C-BC-B4-44-1-2 -4-41-2 2 41) Let C be a basis that contains vectorsThen :and P =C-B-44-422-4 -2 -22b₁ =b₂ =, b3 =, b4=-2-24-4and P =2) Let C be a basis that contains vectors12 36² 3 24 4 and-2 -1-241C-Bb₁ ==b₂ =b3 =b4 =414-1-222−12-211-22-24-4-2 -21 2 2. Then :

By Bartleby policy I have to solve only first one as these are all unrelated & lengthy…

Given basis C, and the change of basis matrix P, determine the basis B. (Hint: what does each column of P represent?) C-B C-B -4 4 -1 -2 -4 -4 2 1 -2 Let C be a basis that contains vectors WEBO and P = C-B Then : -1 4 -4 -2 b₁ = b₂ = , b3 , b4 = 2 4 2 2 2 -2

Given basis C, and the change of basis matrix P, determine the basis B. (Hint: what does each column of P represent?) C-B C-B -4 4 -1 -2 -4 -4 2 1 -2 Let C be a basis that contains vectors WEBO and P = C-B Then : -1 4 -4 -2 b₁ = b₂ = , b3 , b4 = 2 4 2 2 2 -2

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 66E

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Question

Given basis C, and the change of basis matrix P, determine the basis B. (Hint: what does each column of _P_ represent?)
C-B
C-B
4
-4
4
-1
-2 -4
-4
1
-2 2 4
1) Let C be a basis that contains vectors
Then :
and P =
C-B
-4
4
-4
2
2
-4 -2 -2
2
b₁ =
b₂ =
, b3 =
, b4=
-2
-2
4
-4
and P =
2) Let C be a basis that contains vectors
12 36² 3 24 4 and
-2 -1
-2
4
1
C-B
b₁ =
=
b₂ =
b3 =
b4 =
4
1
4
-1
-2
2
2
−1
2
-2
1
1
-2
2
-2
4
-4
-2 -2
1 2 2
. Then :

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