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"If u E R' is a nonzero vector, then there exists a vector v E R° so that the matrix A = (u v) has %3D rank 2."

"If u E R' is a nonzero vector, then there exists a vector v E R° so that the matrix A = (u v) has %3D rank 2."

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Remember - you cannot prove a statement is always true with an example, but you can show a statement is false by providing an example demonstrating it is false. "If u E R' is a nonzero vector, then there exists a vector v E R' so that the matrix A = (u v) has rank 2." (The notation A = (u v) means that the columns of A are the u, v.)**
Transcribed Image Text:Remember - you cannot prove a statement is always true with an example, but you can show a statement is false by providing an example demonstrating it is false. "If u E R' is a nonzero vector, then there exists a vector v E R' so that the matrix A = (u v) has rank 2." (The notation A = (u v) means that the columns of A are the u, v.)**
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