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Unformatted text preview: A Factorization Review A major theme in the linear algebra course has been the interpretation and computation of matrix factorizations ( A = LU , rref ( A ) , A = LDL T , etc.). One way to summarize the course is to review aspects of those factorizations and their uses. A list of tasks is given below. Use your understanding of the course material and the text, and fill in the details as one way of preparing for the final examination. 1. The LU factorization is written as A = LU and A may be rectangular. Describe the main properties of L and U . What are the sizes of L and U in terms of the size of A ? See section 2.6. 2. Describe two legitimate uses of the LU decomposition in applied problems. See sections 2.6 and 5.1. 3. Evaluate det ( A 2 ) when A = 1 5 1 3 1 1 5 1 2 9 8 7 3 / 2 4 3 4 / 3 2 5 / 4 . 4. Find a basis for the nullspace N ( A ) when A = 1 5 1 3 1 1 5 1 2 4 8 2 4 6 . 5. The LDL T factorization is a refinement of the LU factorization and we generally write A = LDL T . Describe the main properties of A , L , and D . See section 2.7....
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