09-08-10

# 09-08-10 - Math 54 Discussion Section Problems Mike...

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Math 54 Discussion Section Problems Mike Hartglass September 8, 2010 You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you aren’t expected to ﬁnish everything. In fact, the answers are largely unimportant; making sure everyone in your group knows how to solve all the problems is what really matters. 1.) Determine if the following sets of vectors are linearly independent or linearly dependent. { (3 , 1 , - 5); (3 , 2 , 4) } { (1 , 2 , 0); (4 , 4 , 3); (0 , 0 , 0) } { (1 , - 1 , 2); (1 , 0 , 1); (3 , - 1 , 4) } 2.) Determine if the following statements about span and linear independence are true or false. If true, prove it and if false, give a concrete counterexample. a. ) If { -→ v 1 , -→ v 2 , -→ v 3 , -→ v 4 } is linearly independent then { -→ v 1 , -→ v 2 , -→ v 3 } is linearly independent. b. ) If { -→ v 1 , -→ v 2 , -→ v 3 , -→ v 4 } is linearly dependent in then { -→ v 1 , -→ v 2 , -→ v 3 } is linearly dependent. c.

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09-08-10 - Math 54 Discussion Section Problems Mike...

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