Math416_Midterm2_Practice

# Math416_Midterm2_Practice - Math 416 Abstract Linear...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 416 - Abstract Linear Algebra Fall 2011, section E1 Practice midterm 2 Name: • This is a (long) practice exam. The real exam will consist of 4 problems. • In the real exam, no calculators, electronic devices, books, or notes may be used. • Show your work. No credit for answers without justification. • Good luck! 1. /15 2. /10 3. /10 4. /10 5. /5 6. /10 7. /15 8. /10 9. /10 10. /10 11. /10 12. /5 Total: /120 1 Section 2.5 Problem 1. Let A be an m × n matrix. a. (5 pts) Show that A has linearly independent columns if and only if A : R n → R m preserves linear independence, in the following sense: For any collection of vectors v 1 , . . ., v k ∈ R n we have { v 1 , . . ., v k } is linearly independent ⇒ { Av 1 , . . ., Av k } is linearly independent. 2 b. (5 pts) Show that A : R n → R m preserves linear independence if and only if for every subspace S ⊆ R n we have dim AS = dim S ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 16

Math416_Midterm2_Practice - Math 416 Abstract Linear...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online