MA326_2011FALL_EXAM2__[0]

# MA326_2011FALL_EXAM2__[0] - Ma326 Linear Algebra Name Fall...

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Unformatted text preview: Ma326 Linear Algebra Name Fall 2011 Exam 2 Show all of your work and all of your answers in your bluebook. When you are finished, hand in this question sheet together with your bluebook. Good luck. (1) (10pts) Suppose A ∈ M m × n ( F ) and B ∈ M n × p ( F ). Prove that rank ( AB ) ≤ min ( { rank ( A ) ,rank ( B ) } ). (2) (12pts) A is a 3 × 3 matrix and b is a 3 × 1 matrix such that the system Ax = b is solved by 1 2- 2 and - 2 1 , but not by 1 2 . Determine which of the following statements (if any) are certainly true based on the given information, which (if any) are certainly false, and which (if any) could be true or false. (Justify your answers.) (a) Ax = 0 has infinitely many solutions. (b)- A 5- 2 = b (c) 3 2 fails to solve the system Ax = b . (d) 1 3 fails to solve the system Ax = b ....
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MA326_2011FALL_EXAM2__[0] - Ma326 Linear Algebra Name Fall...

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