m526t1_pract_s10

m526t1_pract_s10 - A to solve 3 6 9-15-25-55 21 57 40 x 1 x...

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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.
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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 .
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(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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m526t1_pract_s10 - A to solve 3 6 9-15-25-55 21 57 40 x 1 x...

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