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

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Unformatted text preview: 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: 3x1 + 4x2 - x3 + 2x4 = 6 x1 - 2x2 + 3x3 + x4 = 2 10x2 - 10x3 - x4 = 1 2. Suppose you solve Ax = b for three special right sides: 1 0 0 Ax1 = 0 , Ax2 = 1 , Ax3 = 0 , 0 0 1 and that you have determined unique solutions. Then, express A-1 in terms of the variables/parameters that have been introduced thus far. 3. Consider the matrix: -13 -8 -4 A = 12 7 4 . 24 16 7 D = S -1 AS. This matrix is known to be similar to a diagonal matrix D with relation of Determine such D and S. (Please do not use computational methods/software) 4. Determine whether or not the following matrix it. Otherwise, explain why. -1 1 12 1 B= 6 5 3 -4 is diagonalizable. If it is, then diagonalize -2 -4 4 9 -2 -4 5 10 (Hint: it is known that 2 is an eigenvalue of B.) 5. Suppose that A and B are similar matrices. (a) Prove that A3 and B 3 are similar matrices. (b) Suppose also that A is non-singular. Prove that A-1 and B -1 are similar. 6. Prove that if is an eigenvalue of non-singular matrix A, then 1 is an eigenvalue of A-1 . 1 ...
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This note was uploaded on 03/19/2012 for the course AEROSPACE mae260 taught by Professor Park,seung-o&han-limchoi during the Spring '12 term at Korea Advanced Institute of Science and Technology.

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