1. Recall that the image of the elementary vectors e; determines column i. Find the matrix th represents the given transformation. (a) T T: R² → R² where e₁ + [2] (b) T: R² R³ where e₁ (c) T: R² R² where T( [ > T([212₂] = [ T¶ (d) T: R² R³ where T( and e₂ → 1 2 and e₂ → 3 3 [³] (3) - 3 1 5 ₁ + 3x₂ 2x1 + 1x₂ I₁ + 3x₂ 2x₁ + 1₂ 3x1 + 5x2 ]
1. Recall that the image of the elementary vectors e; determines column i. Find the matrix th represents the given transformation. (a) T T: R² → R² where e₁ + [2] (b) T: R² R³ where e₁ (c) T: R² R² where T( [ > T([212₂] = [ T¶ (d) T: R² R³ where T( and e₂ → 1 2 and e₂ → 3 3 [³] (3) - 3 1 5 ₁ + 3x₂ 2x1 + 1x₂ I₁ + 3x₂ 2x₁ + 1₂ 3x1 + 5x2 ]
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...
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![1. Recall that the image of the elementary vectors e; determines column i. Find the matrix th
represents the given transformation.
(a) T T: R² → R² where e₁ + [2]
(b) T: R² R³ where e₁
(c) T: R² R² where T(
[
> T([212₂] = [
T¶
(d) T: R² R³ where T(
and e₂ →
1
2 and e₂ →
3
3
[³]
(3) -
3
1
5
₁ + 3x₂
2x1 + 1x₂
I₁ + 3x₂
2x₁ + 1₂
3x1 + 5x2
]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e6fa127-a003-469d-9a51-b1d4610918ed%2F75eef1f3-7e30-4a49-8f73-8c462cd4682f%2Ffa7vqz_processed.png&w=3840&q=75)
Transcribed Image Text:1. Recall that the image of the elementary vectors e; determines column i. Find the matrix th
represents the given transformation.
(a) T T: R² → R² where e₁ + [2]
(b) T: R² R³ where e₁
(c) T: R² R² where T(
[
> T([212₂] = [
T¶
(d) T: R² R³ where T(
and e₂ →
1
2 and e₂ →
3
3
[³]
(3) -
3
1
5
₁ + 3x₂
2x1 + 1x₂
I₁ + 3x₂
2x₁ + 1₂
3x1 + 5x2
]
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