Let T (tij) be the 7 x 7 matrix with (i, j)-entry tij given by = ti,i+1 = 1, 1 ≤ i ≤ 6, tij s the collection of matrices = = 0 for all other i, j. {T, T², T³, T4, T5, T6} inearly independent? Justify your answer.
Let T (tij) be the 7 x 7 matrix with (i, j)-entry tij given by = ti,i+1 = 1, 1 ≤ i ≤ 6, tij s the collection of matrices = = 0 for all other i, j. {T, T², T³, T4, T5, T6} inearly independent? Justify your answer.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
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![Let T = (tij) be the 7 x 7 matrix with (i, j)-entry tij given by
ti,i+1 = 1, 1 ≤ i ≤ 6, tij = 0 for all other i, j.
Is the collection of matrices
{T, T², T³, T4, T5, T6}
linearly independent? Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5092d283-37fd-4762-962c-92db43347004%2F520bf533-6475-48e5-8d3c-13f3aaabd5d0%2Fxy2jvm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let T = (tij) be the 7 x 7 matrix with (i, j)-entry tij given by
ti,i+1 = 1, 1 ≤ i ≤ 6, tij = 0 for all other i, j.
Is the collection of matrices
{T, T², T³, T4, T5, T6}
linearly independent? Justify your answer.
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