20f-sample-mt1

# 20f-sample-mt1 - n m . MATH. 20F SAMPLE MIDTERM 1 3 (3) (15...

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MATH. 20F SAMPLE MIDTERM 1 You have 50 minutes for this exam. Please write legibly and show all working. No calculators are allowed. Write your name and ID number. Name: ID Number: (1) Let A = 1 2 1 1 a 0 2 1 3 . (i) (8 points) Find all a ’s such that the homogeneous system Ax = 0 has non-trivial solutions. (ii) (7 points) For those values of a from (i), ±nd the general solution of Ax = 0. 1

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2 MATH. 20F SAMPLE MIDTERM 1 (2i) (5 points) Let T : R n R m be a linear transformation. If x and y in R n satisFes T ( x ) = 0 = T ( y ) , show that T ( x + y ) = 0 = T ( λx ) for any scalar λ . (ii) (5 points) If T is one-to-one, show that

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Unformatted text preview: n m . MATH. 20F SAMPLE MIDTERM 1 3 (3) (15 points) Find the inverse of the matrtix A = 1 0 1 0 0 2 2 1 1 , and express A as a product of elementary matrices. 4 MATH. 20F SAMPLE MIDTERM 1 (4) (10 points) Decide if the following statements are true or false, giving justiFcations to your answers. (a) If A is an n n matrix such that A 2 = A A = 0, then A = 0. (b) Any collection of 3 vectors in R 3 such that none is a multiple of another must be linearly independent....
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## This note was uploaded on 03/17/2011 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.

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20f-sample-mt1 - n m . MATH. 20F SAMPLE MIDTERM 1 3 (3) (15...

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