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linear alg extra credit

# linear alg extra credit - R 4 and give an example of four...

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Name Mathematics 364 Extra Credit 1 (Due Monday 3/10/08) Directions: To get the full 5 points, the problems must be all correct or nearly so. Most are short and easy to do. Feel free to ask questions on any of the problems. 1. (a) Find the LU factorization of A = 1 3 4 0 3 5 - 5 - 12 0 . (b) Multiply L by U . If your result doesn’t equal A , you either multiplied wrong or messed up the previous problem. Go back and fix your mistakes. 2. Show that if AB - 1 C = XY Z , then B = CZ - 1 Y - 1 X - 1 A . Then show that B = C ( XY Z ) - 1 A . Assume each matrix is invertible. (Turn over)

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3. Consider the system of equations x + 2 y = 8 and 2 x - 9 y = 16. Without actually solving the equations, determine if x = 2, y = 3 is a solution. 4. Give an example of four vectors that span
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Unformatted text preview: R 4 , and give an example of four vectors that don’t span R 4 . Please explain why your examples work. 5. At the pet store, mice cost 25 cents apiece, hamsters cost a dollar apiece, and guinea pigs cost \$15 apiece. A hungry cat goes into the the store and buys some of each. The cat buys at least one of each, and buys nothing else, spending a total of \$100 on exactly 100 animals. How many of each did the cat buy? [You can do this by setting up two equations and row reducing. There will be a free variable in the solution. You will need to choose the value of the free variable so that solutions are whole numbers.]...
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linear alg extra credit - R 4 and give an example of four...

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