[4 pts] Suppose you know that A is a 4x4 matrix with rank 4. Define a matrix transformation T: R¹ R¹ by T(x) = Ax. Which of the following statements must be true? (Check all that apply.) A is invertible. The nullity of A is 0. 0 is not an eigenvalue of A. A is diagonalizable.
[4 pts] Suppose you know that A is a 4x4 matrix with rank 4. Define a matrix transformation T: R¹ R¹ by T(x) = Ax. Which of the following statements must be true? (Check all that apply.) A is invertible. The nullity of A is 0. 0 is not an eigenvalue of A. A is diagonalizable.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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![[4 pts] Suppose you know that A is a 4x4 matrix with rank 4. Define a matrix transformation
T: Rª → R¹ by T(x) = Ax. Which of the following statements must be true? (Check all
that apply.)
A is invertible.
The nullity of A is 0.
0 is not an eigenvalue of A.
A is diagonalizable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6195f099-697f-489e-94ae-c77f1a063c08%2Fd45c2789-ccd9-4f1a-beb7-26c1d17b4f9d%2Fzb24saw_processed.png&w=3840&q=75)
Transcribed Image Text:[4 pts] Suppose you know that A is a 4x4 matrix with rank 4. Define a matrix transformation
T: Rª → R¹ by T(x) = Ax. Which of the following statements must be true? (Check all
that apply.)
A is invertible.
The nullity of A is 0.
0 is not an eigenvalue of A.
A is diagonalizable.
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