Q1. Given B = {vì = (0, 1, 1, 1), v2 = (2, 1, – 1, –1), v3 = (1,4, – 1,2), v4 = (6,9, 4, 2)} B' = {wi = (0, 8, 8), wz = (-7,8, 1), wz = (-6,9, 1)} 3 -2 1 0 A = 1 6 2 1 -3 0 7 1 and T : R' → R³ such that matrix A is the transformation matrix in relation to B and B' basis. a)Verify that set B is a basis of Rʻand that the set B' is a basis of R³. b}Find [T(v1)]s", [T(v2)]g [T(v3)]ø, [T(va)]& c)find T(v1), T(v2), T(v3), T(v4)
Q1. Given B = {vì = (0, 1, 1, 1), v2 = (2, 1, – 1, –1), v3 = (1,4, – 1,2), v4 = (6,9, 4, 2)} B' = {wi = (0, 8, 8), wz = (-7,8, 1), wz = (-6,9, 1)} 3 -2 1 0 A = 1 6 2 1 -3 0 7 1 and T : R' → R³ such that matrix A is the transformation matrix in relation to B and B' basis. a)Verify that set B is a basis of Rʻand that the set B' is a basis of R³. b}Find [T(v1)]s", [T(v2)]g [T(v3)]ø, [T(va)]& c)find T(v1), T(v2), T(v3), T(v4)
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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![Q1. Given
B = {vi = (0, 1, 1, 1), v2 = (2, 1, –1, -1), v3 = (1, 4, –1, 2), v4 = (6, 9, 4, 2)}
%3!
%3D
B' = {wi = (0, 8, 8), w2 = (-7,8, 1), w3 = (-6,9, 1)}
-2 1
6 2 1
-3 0 7 1
A =
1
and T : R4 → R3 such that matrix A is the transformation matrix in relation to B and B' basis.
a)Verify that set B is a basis of R*and that the set B' is a basis of R³.
b)Find [T(v1)]B, [T(v2)]B [T(v3)]B, [T(v4)]B
c) find
T(v1), T(v2), T(v3), T(v4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9335756d-5405-4a87-94d1-82193f9b3816%2Ff64904c6-324f-4298-be9e-037caf261a76%2Fch4khtn_processed.png&w=3840&q=75)
Transcribed Image Text:Q1. Given
B = {vi = (0, 1, 1, 1), v2 = (2, 1, –1, -1), v3 = (1, 4, –1, 2), v4 = (6, 9, 4, 2)}
%3!
%3D
B' = {wi = (0, 8, 8), w2 = (-7,8, 1), w3 = (-6,9, 1)}
-2 1
6 2 1
-3 0 7 1
A =
1
and T : R4 → R3 such that matrix A is the transformation matrix in relation to B and B' basis.
a)Verify that set B is a basis of R*and that the set B' is a basis of R³.
b)Find [T(v1)]B, [T(v2)]B [T(v3)]B, [T(v4)]B
c) find
T(v1), T(v2), T(v3), T(v4)
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