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1502Test3 - Name Teaching Assistant Math 1502J Andrew 20...

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Name 20 Aprl 2006 Teaching Assistant Hour Test 3 Math 1502J Andrew Instructions: 1. Closed book. 2. Show your work and explain your answers and reasoning. 3. Calculators may be used, but pay particular attention to instruction 2. To receive credit, you must show your work. Unexplained answers, and answers not supported by the work you show, will not receive credit. 4. Express your answers in simplified form. 1. (25) Find a basis for the image and a basis for the kernel of the matrix - = 3 0 2 2 1 2 2 1 0 0 4 0 3 4 2 1 0 1 2 1 A . Compute the dimension of the image and the dimension of the kernel. 2. (25) Find the QR factorization of the matrix = 4 2 1 0 2 2 2 0 1 A by applying the Gram- Schmidt process to the columns of A . 3. (25) A matrix A has QR factorization - - - - = = 1 0 3 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 R Q A .
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