fa11_mae260_hw5 - MAE 260 Homework Assignment#4 Issued Nov...

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MAE 260. Homework Assignment #4 Issued: Nov. 30, 2011 Due: Dec. 8, 2011 (in class) 1. Find all solutions to the system of linear equation: 3 x 1 + 4 x 2 - x 3 + 2 x 4 = 6 x 1 - 2 x 2 + 3 x 3 + x 4 = 2 10 x 2 - 10 x 3 - x 4 = 1 2. Suppose you solve A x = b for three special right sides: A x 1 = ± ² ² ² ² ² ³ 1 0 0 ´ µ µ µ µ µ , A x 2 = ± ² ² ² ² ² ³ 0 1 0 ´ µ µ µ µ µ ,A x 3 = ± ² ² ² ² ² ³ 0 0 1 ´ µ µ µ µ µ , and that you have determined unique solutions. Then, express A - 1 in terms of the vari- ables/parameters that have been introduced thus far. 3. Consider the matrix: A = ± ² ² ² ² ² ³ - 13 - 8 - 4 12 7 4 24 16 7 ´ µ µ µ µ µ . This matrix is known to be similar to a diagonal matrix D with relation of D = S - 1 AS. Determine such D and S . (Please do not use computational methods/software) 4. Determine whether or not the following matrix is diagonalizable. If it is, then diagonalize
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