Exercise 5.5.8 Explain why an nxn matrix A is both one to one and onto if and only if its rank is n.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.2: Addition And Subtraction Of Matrices
Problem 13E
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Exercise 5.5.8 Explain why an n ×n matrix A is both one to one and onto if and only if its rank is n.
Transcribed Image Text:Exercise 5.5.8 Explain why an n ×n matrix A is both one to one and onto if and only if its rank is n.
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