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Unformatted text preview: Mathematics 205  Final Examination Solve all of the twelve problems by using any method learned in Math 205. Please show all work to support your solutions. Our policy is that if you show no supporting work, you will receive no credit. This is a closed book test. Please close your textbook, notebook, cell phone. No calculators are allowed in this test. Please do not start working before you are told to do so. Use the back of each page if necessary. 1. (10 points) Solve the following system of linear equations for all solutions 1 1 1 2 2 1 1 1 1 x y z = 2 5 2 2. (15 points) Let A = 2 2 2 2 2 2 2 2 2 . Find the inverse matrix A − 1 . 3. (10 points) Show that 1 2 3 , 2 3 1 , 3 1 2 forms a basis of R 3 . 4. (10 points) Find all eigenvalues and all eigenvectors of the matrix 3 0 0 3 3 0 3 3 3 ....
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This note was uploaded on 10/03/2011 for the course MATH 205 taught by Professor Zhang during the Spring '08 term at Lehigh University .
 Spring '08
 zhang
 Math

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