Final_Exam_Winter_Quarter_2010-03-19

# Final_Exam_Winter_Quarter_2010-03-19 - 22A Section 001...

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22A Section 001 Final Exam March 19, 2010 Name ID USE OF TEXTS, NOTES OR CALCULATORS IS NOT ALLOWED. Problem Points Score 1 10 2 10 3 10 4 25 5 30 6 20 7 10 8 35 9 10 10 20 11 20 Total 200 Extra Credit 1 10 Extra Credit 2 10 TRY THIS TEST TAKING STRATEGY Here is a good test taking strategy. Do the easy problems ﬁrst! Read over the entire test doing only those problems whose solution is immediately apparent to you. Then make a second pass at the test trying to solve the easiest of the remaining problems. Continue in this way until you are done. Good luck! 0

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22A Section 001 Final Exam March 19, 2010 1. (10 points total) Suppose that I tell you that the n × n matrix A is NONSINGULAR . List TEN conditions that are equivalent to A being nonsingular. I have written the ﬁrst condition – which is one free point – for you. (i) A is nonsingular. (ii) (1.0 point) (iii) (1.0 point) (iv) (1.0 point) (v) (1.0 point) (vi) (1.0 point) (vii) (1.0 point) (viii) (1.0 point) (ix) (1.0 point) (x) (1.0 point) 1
22A Section 001 Final Exam March 19, 2010 2. (10 points) List 10 properties of determinants. (i) (1.0 point) (ii) (1.0 point) (iii) (1.0 point) (iv) (1.0 point) (v) (1.0 point) (vi) (1.0 point) (vii) (1.0 point) (viii) (1.0 point) (ix) (1.0 point) (x) (1.0 point) 2

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22A Section 001 Final Exam March 19, 2010 3. (10 points) Let A be any N × M matrix. Which of the following statements are always True or False (You do not have to give a reason for your answer.) (i) (1.0 point) The column space of A is the same as the range of A, R (A). (ii) (1.0 point) The row space of A is the same as the column space A . (iii) (1.0 point) rank + nullity = N . (iv) (1.0 point) The dimension of the row space of A and the dimension of the column space of A are always the same. (v) (1.0 point) The range of A,
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Final_Exam_Winter_Quarter_2010-03-19 - 22A Section 001...

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