True or false? If true, explain why. If false, give a counterexample or expla- nation.
True or false? If true, explain why. If false, give a counterexample or expla- nation.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 10AEXP
Related questions
Question
True or false? If true, explain why. If false, give a counterexample or expla-
nation.
![(a) If i = [1 0 -2| is an eigenvector of A, then 20 = |2 0 -4] is also an eigenvector
of A.
(b) The eigenvalues of A are on its main diagonal.
(c) The nullity of A is the number of columns in the reduced echelon form of A that
do not contain leading ones.
(d) A 3 x 5 matrix A whose reduced echelon form has 2 leading ones has nullity 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa40747ab-a715-4b8f-ac3d-96cea976aaee%2F68a07075-ce73-4955-a554-2c091a21fdf5%2F4tsbx2q_processed.png&w=3840&q=75)
Transcribed Image Text:(a) If i = [1 0 -2| is an eigenvector of A, then 20 = |2 0 -4] is also an eigenvector
of A.
(b) The eigenvalues of A are on its main diagonal.
(c) The nullity of A is the number of columns in the reduced echelon form of A that
do not contain leading ones.
(d) A 3 x 5 matrix A whose reduced echelon form has 2 leading ones has nullity 2.
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