Suppose : R¹ R² is a linear transformation and f(en) = a, for n=1,2,3. A= 02 1 -1 -2 e. The inear transformation f is (select all that apply): DA surjective (onto) a2 B. injective (one-to-one) C. bjective (an isomorphism) D. none of these -3-2-1 M Domain a. Find a formula for f. Your answer should be a coordinate vector with the variables z, y, and z in its components. f(z, y, z)= ak Codomain a3 b. Find matrix for the linear transformation f (relative to the standard basis in the domain and codomain). That is, find the matrix A such that f(x)= Ax. For instance, enter [ [1 2] [1,2] [3,4]] for the matrix 2 3 c. Find the kernel of f. Enter your answer as a vector with constant entries, a vector with the variables ar, y, z in its components (using a minimum number of variables), or enter R^3. for R ker (f) - d. Find the image of f. Enter your answer as a vector with constant entries, a vector with the variables ar, y, z in its components (using a minimum number of variables), or enter R^2 for R². im(f)
Suppose : R¹ R² is a linear transformation and f(en) = a, for n=1,2,3. A= 02 1 -1 -2 e. The inear transformation f is (select all that apply): DA surjective (onto) a2 B. injective (one-to-one) C. bjective (an isomorphism) D. none of these -3-2-1 M Domain a. Find a formula for f. Your answer should be a coordinate vector with the variables z, y, and z in its components. f(z, y, z)= ak Codomain a3 b. Find matrix for the linear transformation f (relative to the standard basis in the domain and codomain). That is, find the matrix A such that f(x)= Ax. For instance, enter [ [1 2] [1,2] [3,4]] for the matrix 2 3 c. Find the kernel of f. Enter your answer as a vector with constant entries, a vector with the variables ar, y, z in its components (using a minimum number of variables), or enter R^3. for R ker (f) - d. Find the image of f. Enter your answer as a vector with constant entries, a vector with the variables ar, y, z in its components (using a minimum number of variables), or enter R^2 for R². im(f)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Advanced Math
![Suppose f: R³-R² is a linear transformation and f(e) = a, for n=1,2,3.
A=
€2
Y
1
e. The inear transformation f is (select all that apply):
DA. surjective (onto)
-1
-2
B. injective (one-to-one)
C. bjective (an isomorphism)
D. none of these
a2
-3-2-1
M
Domain
a. Find a formula for f. Your answer should be a coordinate vector with the variables z, y, and z in its components.
f(z, y, z)=
ak
Codomain
a3
b. Find t matrix for the linear transformation f (relative to the standard basis in the domain and codomain). That is, find the matrix A such that f(x)= Ax. For instance, enter [
[1 2]
[1,2] [3,4]] for the matrix
2
3
c. Find the kernel of f. Enter your answer as a vector with constant entries, a vector with the variables ar, y, z in its components (using a minimum number of variables), or enter R^3.
for R².
ker (f) -
d. Find the image of f. Enter your answer as a vector with constant entries, a vector with the variables , y, z in its components (using a minimum number of variables), or enter R^2
for R².
im(f)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b52ec0e-1718-4a1e-8f5b-618ac05e1ee0%2F6c747177-f9c1-4831-b065-7bcd16feaaca%2Fx5hgfgc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose f: R³-R² is a linear transformation and f(e) = a, for n=1,2,3.
A=
€2
Y
1
e. The inear transformation f is (select all that apply):
DA. surjective (onto)
-1
-2
B. injective (one-to-one)
C. bjective (an isomorphism)
D. none of these
a2
-3-2-1
M
Domain
a. Find a formula for f. Your answer should be a coordinate vector with the variables z, y, and z in its components.
f(z, y, z)=
ak
Codomain
a3
b. Find t matrix for the linear transformation f (relative to the standard basis in the domain and codomain). That is, find the matrix A such that f(x)= Ax. For instance, enter [
[1 2]
[1,2] [3,4]] for the matrix
2
3
c. Find the kernel of f. Enter your answer as a vector with constant entries, a vector with the variables ar, y, z in its components (using a minimum number of variables), or enter R^3.
for R².
ker (f) -
d. Find the image of f. Enter your answer as a vector with constant entries, a vector with the variables , y, z in its components (using a minimum number of variables), or enter R^2
for R².
im(f)
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