Math 33A, Midterm 1 solutions1. We frst write the augmented coeﬃcient matrix and then perForm Gauss-Jordan elimi-nations (row operations):±12−|336−10|5²subtract 3 times row I From row II±−|300 2−6|−4²divide row II by 2±−|300 1−32²add row II to row I±120−1|1001−32²±rom the RRE± we see that variablesyandware going to be arbitrary parameters,whilexandzare going to be expressed in terms oF these parameters. We successivelywrite:w=s,z=3s−2,y=t,x=−2t+s+1,For arbitrary real parameterssandt. We can also write the solution in the Form⎛⎜⎜⎝xyzw⎞⎟⎟⎠=⎛⎜⎜⎝−2t+st3s−2s⎞⎟⎟
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