(1 point) The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are shown in the figures below. a. Find the change of basis matrix from custom B-coordinates to standard S-coordinates. [id] = id= -2 b Find the change of basis matrix from custom C-coordinates to standard S-coordinates [id] = -1 c. Find the change of basis matrix from B-coordinates to C-coordinates -1 -3 -1/12 1/4 d. Find the change of basis matrix from C-coordinates to B-coordinates. Standard basis S= {0₁,0₂) 4 3 2 1 -1 -2 -9 b2 -3-2-1 62 el bl 1 2 3 b1 X Custom basis B = {b₁,b₂} |id|s [id Standard basis S= (0₁,0₂} M 3 2 i -1 -2 -9 c2 -3-2-1 G2 162 27 el [id] ↑ c1 1 2 2 3 01 H X Custom basis C (C₁, C₂)
(1 point) The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are shown in the figures below. a. Find the change of basis matrix from custom B-coordinates to standard S-coordinates. [id] = id= -2 b Find the change of basis matrix from custom C-coordinates to standard S-coordinates [id] = -1 c. Find the change of basis matrix from B-coordinates to C-coordinates -1 -3 -1/12 1/4 d. Find the change of basis matrix from C-coordinates to B-coordinates. Standard basis S= {0₁,0₂) 4 3 2 1 -1 -2 -9 b2 -3-2-1 62 el bl 1 2 3 b1 X Custom basis B = {b₁,b₂} |id|s [id Standard basis S= (0₁,0₂} M 3 2 i -1 -2 -9 c2 -3-2-1 G2 162 27 el [id] ↑ c1 1 2 2 3 01 H X Custom basis C (C₁, C₂)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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JUST NEED HELP ON C AND D. Write down the solution neatly and clearly please.
![(1 point)
The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are shown in the figures below.
a. Find the change of basis matrix from custom B-coordinates to standard S-coordinates.
[id] =
b Find the change of basis matrix from custom C-coordinates to standard S-coordinates
id=
c. Find the change of basis matrix from B-coordinates to C-coordinates
[id] =
-1/12
1/4
d. Find the change of basis matrix from C-coordinates to B-coordinates.
Standard basis S= {0₁, 0₂}
4
3
2
1
-1
-2
-9
to
b2
-3-2-1
29
el
bl
1 2 3
V
b1
X
Custom basis B = {b₁,b₂}
|id|s
[id
Standard basis S= (0₁,0₂}
3
2 02
1
-1
-2
-9
-3-2-1
G2
162
27
Au
el
[id] ↑
cl
12 2 3
61
H
x
Custom basis C (C₁, C₂)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b7533f2-c4c9-4e07-81d6-1cc62935d4d9%2F498949a2-3df1-4515-a251-391ee6c6c610%2F94ea6j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(1 point)
The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are shown in the figures below.
a. Find the change of basis matrix from custom B-coordinates to standard S-coordinates.
[id] =
b Find the change of basis matrix from custom C-coordinates to standard S-coordinates
id=
c. Find the change of basis matrix from B-coordinates to C-coordinates
[id] =
-1/12
1/4
d. Find the change of basis matrix from C-coordinates to B-coordinates.
Standard basis S= {0₁, 0₂}
4
3
2
1
-1
-2
-9
to
b2
-3-2-1
29
el
bl
1 2 3
V
b1
X
Custom basis B = {b₁,b₂}
|id|s
[id
Standard basis S= (0₁,0₂}
3
2 02
1
-1
-2
-9
-3-2-1
G2
162
27
Au
el
[id] ↑
cl
12 2 3
61
H
x
Custom basis C (C₁, C₂)
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