True or false? If true, explain why. If false, give a counterexample or expla- nation.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
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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