3. Let B= b₁ b2 b3 be a basis for R3 and let v = (a) Find [v], the coordinate vector of v with respect to the B-basis. R₁-R2 R₂-R3 00 2 01 0 " [v]B] (b) Suppose T: R3 R2 is the linear transformation satisfying T(b₁) = [52] = [2] T(b₂)= | [21]. T(bs) = ====== [3] Find T(v). HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B?
3. Let B= b₁ b2 b3 be a basis for R3 and let v = (a) Find [v], the coordinate vector of v with respect to the B-basis. R₁-R2 R₂-R3 00 2 01 0 " [v]B] (b) Suppose T: R3 R2 is the linear transformation satisfying T(b₁) = [52] = [2] T(b₂)= | [21]. T(bs) = ====== [3] Find T(v). HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B?
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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Question
Asking for help on part b
![3. Let B =
b₁
b2
b3
MAT2114 HOMEWORK 06
be a basis for R3 and let v =
(a) Find [v], the coordinate vector of v with respect to the B-basis.
R₁-R₂
12-R3
[v]B
=
0 0
(b) Suppose T: R3 R2 is the linear transformation satisfying
Find T(v).
->
T(b)= [2] Tb2)= [2] T(bs) = [3]
HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY
COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7538180c-5348-4d54-a5c1-c840ed6fc5b5%2F3b6cc7e3-14f9-40e5-8ca9-ace753e25cf3%2Fmxyqqa9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let B =
b₁
b2
b3
MAT2114 HOMEWORK 06
be a basis for R3 and let v =
(a) Find [v], the coordinate vector of v with respect to the B-basis.
R₁-R₂
12-R3
[v]B
=
0 0
(b) Suppose T: R3 R2 is the linear transformation satisfying
Find T(v).
->
T(b)= [2] Tb2)= [2] T(bs) = [3]
HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY
COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B?
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