09-20-10

# 09-20-10 - 3 2 4 0 1-2 0 0 4 Can you ﬁnd det A If yes...

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Math 54 Discussion Section Problems Mike Hartglass September 20, 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. Use row reductions to evaluate ± ± ± ± ± ± ± ± 0 1 5 4 1 - 1 - 3 0 - 1 2 8 5 3 - 1 - 2 3 ± ± ± ± ± ± ± ± by putting it in Echelon form. 2. Solve A x = b for A = 1 5 - 2 0 2 3 - 4 0 8 and b = 1 - 2 1 using Cramer’s rule. 3. If A is an n × n matrix, what is the relationship between det A and det (3 A )? 4. (a) Suppose someone tells you that a matrix A can be row reduced to
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Unformatted text preview: 3 2 4 0 1-2 0 0 4 . Can you ﬁnd det A ? If yes, ﬁnd it; if not, explain why. (b) Repeat part (a) for a matrix that can be reduced to 3 2 4 0 1-2 0 0 5. Use determinants to decide whether 7-4-6 , -8 5 7 , 7-5 are linearly dependent or independent. 6. Prove that if A and B are n × n matrices and AB is invertible then A and B are invertible 7. Prove that if A is a non invertible n × n matrix and B is an arbitrary n × n matrix then AB is not invertible 8. Suppose A in an n × n matrix with A 2 =-I . Prove that n is even....
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