11. Suppose that T: Rª → R6 and S: R6 → R¹? a. Which of the transformations, S or T could be one-to-one? Explain your reasoning. You may use pictures if you would like. b. Which of the transformations, S or T could be onto? Explain your reasoning. You may use pictures if you would like. C. Which of the following ST or TS could be an isomorphism, explain how you know? d. Are P₁ (R) and R² isomorphic? e. Suppose that A is the matrix of the transformation T and A is 4 x 3, can T be onto? f. Suppose that A has the eigenvalue of 6 and a corresponding eigenvector of H -21 is A* 2 ? What g. Let T: V → W be a linear transformation, and A, the matrix of the linear transformation T is 4x6 and the transformation is onto. What is the dimension of KerT?
11. Suppose that T: Rª → R6 and S: R6 → R¹? a. Which of the transformations, S or T could be one-to-one? Explain your reasoning. You may use pictures if you would like. b. Which of the transformations, S or T could be onto? Explain your reasoning. You may use pictures if you would like. C. Which of the following ST or TS could be an isomorphism, explain how you know? d. Are P₁ (R) and R² isomorphic? e. Suppose that A is the matrix of the transformation T and A is 4 x 3, can T be onto? f. Suppose that A has the eigenvalue of 6 and a corresponding eigenvector of H -21 is A* 2 ? What g. Let T: V → W be a linear transformation, and A, the matrix of the linear transformation T is 4x6 and the transformation is onto. What is the dimension of KerT?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter1: Variables, Expressions, And Integers
Section1.3: Order Of Operations
Problem 1E
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can you please solve the problem on the picture, Post pictures of all of your work please.
Transcribed Image Text:11. Suppose that T: R4 R6 and S: R6 → Rª?
a. Which of the transformations, S or T could be one-to-one? Explain your reasoning. You
may use pictures if you would like.
b.
Which of the transformations, S or T could be onto? Explain your reasoning. You may
use pictures if you would like.
C.
Which of the following ST or TS could be an isomorphism, explain how
d. Are P₁(R) and R² isomorphic?
e.
Suppose that A is the matrix of the transformation T and A is 4 x 3, can T be onto?
f.
Suppose that A has the eigenvalue of 6 and a corresponding eigenvector of
is A*
you know?
2
2₂
2 ?
12
What
g.
Let T: V → W be a linear transformation, and A, the matrix of the linear transformation
T is 4x6 and the transformation is onto. What is the dimension of KerT?
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