If A is a 3 x 3 matrix which is diagonalizable and the following. three vectors are eigenvectors for 3 distinct eigenvalues of A, (0, 1, -1)", (2, 0, 3)7, (1, 1, -2)", which of the following vectors could be the first column of a matrix P which diagonalizes A? A) (1, 1, -2)7 (B) (0, 0, 1) (C) (1, 0, 0)7 D) (0, 1, 0) (E) (-1,0, –1)7 (F) (1, 2, -3)7-(G) (0, 1, 1)7 H) (2, 0, -3)7
If A is a 3 x 3 matrix which is diagonalizable and the following. three vectors are eigenvectors for 3 distinct eigenvalues of A, (0, 1, -1)", (2, 0, 3)7, (1, 1, -2)", which of the following vectors could be the first column of a matrix P which diagonalizes A? A) (1, 1, -2)7 (B) (0, 0, 1) (C) (1, 0, 0)7 D) (0, 1, 0) (E) (-1,0, –1)7 (F) (1, 2, -3)7-(G) (0, 1, 1)7 H) (2, 0, -3)7
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![If \( A \) is a \( 3 \times 3 \) matrix which is diagonalizable and the following three vectors are eigenvectors for 3 distinct eigenvalues of \( A \),
\[
(0, 1, -1)^T, \, (2, 0, 3)^T, \, (1, 1, -2)^T,
\]
which of the following vectors could be the first column of a matrix \( P \) which diagonalizes \( A \)?
A) \( (1, 1, -2)^T \)
B) \( (0, 0, 1)^T \)
C) \( (1, 0, 0)^T \)
D) \( (0, 1, 0)^T \)
E) \( (-1, 0, -1)^T \)
F) \( (1, 2, -3)^T \)
G) \( (0, 1, 1)^T \)
H) \( (2, 0, -3)^T \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4742c455-7d1e-40c9-8f1c-d13da87d8293%2Fc8bd804a-bc7e-4702-970c-395a38358e7e%2F8jc78cd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If \( A \) is a \( 3 \times 3 \) matrix which is diagonalizable and the following three vectors are eigenvectors for 3 distinct eigenvalues of \( A \),
\[
(0, 1, -1)^T, \, (2, 0, 3)^T, \, (1, 1, -2)^T,
\]
which of the following vectors could be the first column of a matrix \( P \) which diagonalizes \( A \)?
A) \( (1, 1, -2)^T \)
B) \( (0, 0, 1)^T \)
C) \( (1, 0, 0)^T \)
D) \( (0, 1, 0)^T \)
E) \( (-1, 0, -1)^T \)
F) \( (1, 2, -3)^T \)
G) \( (0, 1, 1)^T \)
H) \( (2, 0, -3)^T \)
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