Let ₹₁ = [1; 0; 0], ẻ2 = [0; 1; 0], ẻ3 = [0; 0; 1] denote the standard vectors in R³, and let T: R³ R4 be such that T(₁) 2 -0--0- T(2₂) = 1 = 1 and T(₁ + 3) = -0 = 1 What is the standard matrix A for T?
Let ₹₁ = [1; 0; 0], ẻ2 = [0; 1; 0], ẻ3 = [0; 0; 1] denote the standard vectors in R³, and let T: R³ R4 be such that T(₁) 2 -0--0- T(2₂) = 1 = 1 and T(₁ + 3) = -0 = 1 What is the standard matrix A for T?
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
![Let ₹₁ = [1; 0; 0], ẻ2 = [0; 1; 0], ẻ3 = [0; 0; 1] denote the standard vectors in R³,
and let T: R³
R4 be such that
T(₁)
O
A
A =
=
What is the standard matrix A for T?
(i.e., the matrix so that T(x) = A)
A =
=
=
0 0
1
0
0
1
0
1
01
02 -1
0
0 1
1
T(2₂) =
00 1
2 00
-1 0 1
2
0
0
0 1 -1
-
02 1
00
1
and T(2₁ +23) =
=
0
0 0
O It is not possible to find out A with this information.
1
0
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc72595e-2e96-49e1-8ed0-19a59c149cce%2Fc7eee2af-e2a7-484f-87d8-ed270d739e22%2Fhdqfh1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let ₹₁ = [1; 0; 0], ẻ2 = [0; 1; 0], ẻ3 = [0; 0; 1] denote the standard vectors in R³,
and let T: R³
R4 be such that
T(₁)
O
A
A =
=
What is the standard matrix A for T?
(i.e., the matrix so that T(x) = A)
A =
=
=
0 0
1
0
0
1
0
1
01
02 -1
0
0 1
1
T(2₂) =
00 1
2 00
-1 0 1
2
0
0
0 1 -1
-
02 1
00
1
and T(2₁ +23) =
=
0
0 0
O It is not possible to find out A with this information.
1
0
1
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