MidSol5 - (b) Here we have to nd a linear system whose...

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(b) Here we have to fnd a linear system whose solution is x 1 x 2 x 3 = t 5 2 3 = 5 t 2 t 3 t . From the last row we read o± t = 1 3 x 3 so that x 1 =5 t = 5 3 x 3 , and x 2 =2 t = 2 3 x 3 . This system can be written more nicely as ½ 3 x 1 5 x 3 =0 3 x 2 2 x 3 and corresponds to the matrix (i.e. linear trans²ormation) T = µ 30 5 03 2 . 8. We frst write the augmented coefficient matrix and then per²orm Gauss-Jordan elimi- nations (row operations): 11 1 | 1 12 k | 2 14 k 2 | 3 subtract row I ²rom row II subtract row I ²rom row III 11 1 | 1 01 k 1 | 1 k 2 1 | 2 subtract row II ²rom row I subtract 3 times row II ²rom row III 10 k +2 | 0 k 1 | 1 00 k 2 3 k |− 1 Let us observe that
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This note was uploaded on 04/12/2011 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

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