Consider the ordered bases B = ((-1,7), (1, –8)) and C = ((0, –2), (4, –3)) for the vector space R². a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). 4 TE -2 -3 b. Find the transition matrix from B to E. -1 1 T = | 7 -8 c. Find the transition matrix from E to B. -8 -1 T |-7 -1 d. Find the transition matrix from C to B. e. Find the coordinates of u (-2, –3) in the ordered basis B. Note that [u]B = T {u]E. [u]B = f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]c = (2, 1).
Consider the ordered bases B = ((-1,7), (1, –8)) and C = ((0, –2), (4, –3)) for the vector space R². a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). 4 TE -2 -3 b. Find the transition matrix from B to E. -1 1 T = | 7 -8 c. Find the transition matrix from E to B. -8 -1 T |-7 -1 d. Find the transition matrix from C to B. e. Find the coordinates of u (-2, –3) in the ordered basis B. Note that [u]B = T {u]E. [u]B = f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]c = (2, 1).
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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3.2 Question 6
![e. Find the coordinates of u = (-2, –3) in the ordered basis B. Note that [u]B = Tu]E.
[2] B =
f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]c = (2, 1).
1
[v]B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F326a7328-130e-4258-98d9-f22d8fa27a9c%2Fd8682fcc-0029-485d-9d78-b916b12040ca%2F7oa7auo_processed.png&w=3840&q=75)
Transcribed Image Text:e. Find the coordinates of u = (-2, –3) in the ordered basis B. Note that [u]B = Tu]E.
[2] B =
f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]c = (2, 1).
1
[v]B
![Consider the ordered bases B = ((-1,7), (1, –8)) and C = ((0,–2), (4, –3)) for the vector space R².
a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)).
4
|-2
-3
b. Find the transition matrix from B to E.
1
-1
1
TE
[ 7
-8
c. Find the transition matrix from E to B.
-8
-1
TË
-7
-1
d. Find the transition matrix from C to B.
e. Find the coordinates of u = (-2, –3) in the ordered basis B. Note that [u]B = Tlu] E.
[u]B
f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]c = (2, 1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F326a7328-130e-4258-98d9-f22d8fa27a9c%2Fd8682fcc-0029-485d-9d78-b916b12040ca%2Fk70tl8m_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the ordered bases B = ((-1,7), (1, –8)) and C = ((0,–2), (4, –3)) for the vector space R².
a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)).
4
|-2
-3
b. Find the transition matrix from B to E.
1
-1
1
TE
[ 7
-8
c. Find the transition matrix from E to B.
-8
-1
TË
-7
-1
d. Find the transition matrix from C to B.
e. Find the coordinates of u = (-2, –3) in the ordered basis B. Note that [u]B = Tlu] E.
[u]B
f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]c = (2, 1).
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