e. If H is a subspace of R", then there is a nxn matrix A such that H = Col A. f. If A is m x n matrix and rank A is equal to m, then the linear transformation H A is injective. g. If A is m x n matrix and the linear transformation + AT is surjective, then rank of A is equal to m.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Exercise 3.
Mark each statement True of False: Justify each answer. (if true, cite appropriate
facts or theorems. If false, explain why or give a counterexample that shows why
the statement is not true in every case)
HOua lin0onlu
don
Hont
Transcribed Image Text:Exercise 3. Mark each statement True of False: Justify each answer. (if true, cite appropriate facts or theorems. If false, explain why or give a counterexample that shows why the statement is not true in every case) HOua lin0onlu don Hont
e. If H is a subspace of R", then there is a n xn matrix A such that H = Col A.
f. If A is m x n matrix and rank A is equal to m, then the linear transformation
n H At is injective.
g. If A is m x n matrix and the linear transformation 7 + AT is surjective,
then rank of A is equal to m.
Transcribed Image Text:e. If H is a subspace of R", then there is a n xn matrix A such that H = Col A. f. If A is m x n matrix and rank A is equal to m, then the linear transformation n H At is injective. g. If A is m x n matrix and the linear transformation 7 + AT is surjective, then rank of A is equal to m.
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