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**Unformatted text preview: **Assignment for Applied Linear Algebra - Math 270 January 14, 2011 Every exercise has the same value. Doing correctly 90% of the whole assignment guarantees full marks. The deadline is set to January 28. (Please see details in the Outline of the course, on WebCT.) Problem 1 Use PLU decomposition (with pivoting if needed) to compute the 1 st and 3 rd columns of A- 1 . The matrix A is given by A := 3- 1 1- 1- 4- 1- 1 4 8 3- 1 1 2 . Detail the steps used for the decomposition (I think that it can’t be done with less than 4 steps). Specify which elementary matrix (or matrices) is (are) used in each step. SOLUTION: Note, PLU decomposition is not unique. One example is P := 1 1 1 1 , L := 1 0 1- 1 1 1- 1 0- 1 2 1 , U := 1- 1- 4- 1 3- 1 4 3 1 2 . Since AA- 1 = I , solving PLUx 1 = e 1 and PLUx 2 = e 3 gives the 1 st and 3 rd columns of A- 1 . Computing Pz 1 = e 1 , Ly...

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