The standard basis S- {e₁. e) and two custom bases B (b₁,b₂} and C (₁.2) for R² are shown in the figures below. Standard basis S = {₁, ₂} N a. Find the change of basis matrix from custom B-coordinates to standard S-coordinates. b. Find the change of basis matrix from custom C-coordinates to standard S-coordinates Tidle 3 2 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. 4 - -2 62 -3-2-1 AN 2 bl x 1 23 Custom basis B (b₁,b₂) [id 1 lid Standard basis S = {0₁₂,0₂} N - -2 -9 -3-2-1 es [idt ci M 1 2 3 Custom basis C-(C₁, C₂)
The standard basis S- {e₁. e) and two custom bases B (b₁,b₂} and C (₁.2) for R² are shown in the figures below. Standard basis S = {₁, ₂} N a. Find the change of basis matrix from custom B-coordinates to standard S-coordinates. b. Find the change of basis matrix from custom C-coordinates to standard S-coordinates Tidle 3 2 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. 4 - -2 62 -3-2-1 AN 2 bl x 1 23 Custom basis B (b₁,b₂) [id 1 lid Standard basis S = {0₁₂,0₂} N - -2 -9 -3-2-1 es [idt ci M 1 2 3 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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![The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are shown in the figures below.
Standard basis S= (₁, ₂)
4
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
-1
-1
c. Find the change of basis matrix from B-coordinates to C-coordinates
-3
-1/12
1/4
d. Find the change of basis matrix from C-coordinates to B-coordinates.
3
2
1
-1
-2
-9
b2
-3-2-1
82
el
bl
1 2 3
b1
X
Custom basis B = {b₁,b₂)
|id|s
[id
Standard basis S= (0₁,0₂}
a
3
2
1
-1
-2
-9
c2
-3 -2 -1
G2
62
217
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%2F252a6f1e-a237-4559-bd75-fd7154845b0a%2Fda91bd35-2335-4da3-a6e2-4e4b64badd3b%2Fjsgx1d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are shown in the figures below.
Standard basis S= (₁, ₂)
4
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
-1
-1
c. Find the change of basis matrix from B-coordinates to C-coordinates
-3
-1/12
1/4
d. Find the change of basis matrix from C-coordinates to B-coordinates.
3
2
1
-1
-2
-9
b2
-3-2-1
82
el
bl
1 2 3
b1
X
Custom basis B = {b₁,b₂)
|id|s
[id
Standard basis S= (0₁,0₂}
a
3
2
1
-1
-2
-9
c2
-3 -2 -1
G2
62
217
el
[id] ↑
cl
12 2 3
61
H
x
Custom basis C (C₁, C₂)
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