m526t1_pract_s10

# m526t1_pract_s10 - A to solve 3 6-55 21 57 40 x 1 x 2 x 3...

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Math. 526 Numerical Linear Algebra Practice Test 1 February 08, 2010 Name There are 6 problems. Show all work. 1. (15 points) Let v = " 9 12 # and w = " 12 - 9 # . Find: (a) v + w (b) The linear combination of v and w with coeﬃcients 2 , - 1. (c) Compute the dot product v · w (d) Compute || v || and || w || (e) Find the angle between the vectors v and w (f) Find a unit vector in the direction of the vector v .

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2. (10) Let A = " 5 - 1 3 5 2 1 # , , and B = " 1 3 5 6 # . Below is a list of matrix products. Circle the ones that are deﬁned and cross the products that are not deﬁned. AB BA AA BB (b) Compute the products that are deﬁned.
3. (15 points) Let A = 1 1 3 2 1 5 2 2 7 . Find A - 1 , the inverse matrix of A .

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4. (25 points) Let A = 3 6 9 - 15 - 25 - 55 21 57 40 . (a) Find the L - U factorization of A .
(b) Use the L - U factorization of

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Unformatted text preview: A to solve 3 6 9-15-25-55 21 57 40 x 1 x 2 x 3 = 3-50-70 . (c) Find the L-D-U factorization of A . 5. (15 points) True or False (a) For any n x n matrices A and B we have BA = ( AB ). (b) If A is not invertible matrix then the equation ABx = always has more than one solution. (c) If A and B are upper triangular n x n matrices then AB is an upper triangular matrix. (d) If A is any diagonal n x n matrix and B is any n x n matrix then AB = BA . (e) If A is an n x n matrix and the linear system Ax = b has two distinct solutions then A is not invertible....
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## This note was uploaded on 06/11/2011 for the course MATH 526 taught by Professor Johnson,g during the Spring '08 term at Columbia SC.

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m526t1_pract_s10 - A to solve 3 6-55 21 57 40 x 1 x 2 x 3...

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