Problem (i) Consider the normalized vector v in R and the permutation matrix P, respectively 0 1 0 0 0 1 1 0 0 P = V3 (:)*-- Are the three vectors v, Pv, P²v linearly independent?
Problem (i) Consider the normalized vector v in R and the permutation matrix P, respectively 0 1 0 0 0 1 1 0 0 P = V3 (:)*-- Are the three vectors v, Pv, P²v linearly independent?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 42EQ
Related questions
Question
![Problem
(i) Consider the normalized vector v in R³ and the permutation
matrix P, respectively
0 1 0
P = | 0 0 1
0 0
1
V3
-1
1
Are the three vectors v, Pv, P²v linearly independent?
(ii) Consider the 4 x 4 symmetric matrix A and the vector b in R4
0 1 0 0
1 0 1 0
0 1 0 1
0 0 1 0
1
b =
1
A =
Are the vectors b, Ab, A²b, A³b in R4 linearly independent? Show that the
matrix A is invertible. Look at the column vectors of the matrix A
O000
1
1
Find the inverse of A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee79dc66-a6d9-422f-83a7-1b5e6206aea6%2F5717e7f7-491c-48e3-86f9-3a5a451b3353%2Fjgwy5hw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem
(i) Consider the normalized vector v in R³ and the permutation
matrix P, respectively
0 1 0
P = | 0 0 1
0 0
1
V3
-1
1
Are the three vectors v, Pv, P²v linearly independent?
(ii) Consider the 4 x 4 symmetric matrix A and the vector b in R4
0 1 0 0
1 0 1 0
0 1 0 1
0 0 1 0
1
b =
1
A =
Are the vectors b, Ab, A²b, A³b in R4 linearly independent? Show that the
matrix A is invertible. Look at the column vectors of the matrix A
O000
1
1
Find the inverse of A.
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