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MidSol5

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

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(b) Here we have to find 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 off 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 3 x 1 5 x 3 = 0 3 x 2 2 x 3 = 0 and corresponds to the matrix (i.e. linear transformation) T = 3 0 5 0 3 2 . 8. We first write the augmented coeﬃcient matrix and then perform Gauss-Jordan elimi- nations (row operations): 1 1 1 | 1 1 2 k | 2 1 4 k 2 | 3 subtract row I from row II subtract row I from row III 1 1 1 | 1 0 1 k 1 | 1 0 3 k 2 1 | 2 subtract row II from row I subtract 3 times row II from row III 1 0 k + 2 | 0 0 1 k 1 | 1 0 0 k 2 3 k + 2 | 1 Let us observe that k 2
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