MAE 260. Homework Assignment #4Issued: Nov. 30, 2011Due: Dec. 8, 2011 (in class)1. Find all solutions to the system of linear equation:3x1+4x2-x3+2x4=6x1-2x2+3x3+x4=210x2-10x3-x4=12. Suppose you solveAx=bfor three special right sides:Ax1=±²²²²²³100´µµµµµ¶, Ax2=±²²²²²³010´µµµµµ¶,Ax3=±²²²²²³001´µµµµµ¶,and that you have determined unique solutions. Then, expressA-1in terms of the vari-ables/parameters that have been introduced thus far.3. Consider the matrix:A=±²²²²²³-13-8-4127424167´µµµµµ¶.This matrix is known to be similar to a diagonal matrixDwith relation ofD=S-1AS.Determine suchDandS. (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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Diagonalizable matrix, Diagonal matrix, similar matrices, special right sides