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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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 :
Transcribed Image Text: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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