mat22a-practiceexam2

# mat22a-practiceexam2 - Math 22A UC Davis Winter 2011 Prof...

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Math 22A UC Davis, Winter 2011 Prof. Dan Romik Practice questions for the 2/16 midterm 1. (a) Deﬁne A = 1 3 - 1 1 4 - 1 - 1 - 3 2 . Compute the inverse matrix of A . (b) Find the solution v = x y z to the equation Av = 2 - 1 0 . 2. Compute the following determinants: (a) det ± 1 2 3 k ² (c) det 0 1 0 0 0 1 0 0 0 0 0 0 1 0 2 0 0 0 4 - 2 0 0 3 1 0 (b) det 1 0 2 0 4 - 2 3 1 0 (d) det( A 3 ) where A = 2 0 0 13 2 0 - 19 1001 - 1 3. Let σ be the permutation ± 1 2 3 4 5 6 2 3 1 6 5 4 ² of order 6. (a) Find the sign sgn( σ ) of the permutation. Explain your answer — a guess with no explanation is not a valid answer. (b) Find the inverse permutation

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mat22a-practiceexam2 - Math 22A UC Davis Winter 2011 Prof...

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