MidSol1 - Math 33A, Midterm 1 solutions 1. We rst write the...

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Math 33A, Midterm 1 solutions 1. We frst write the augmented coefficient matrix and then perForm Gauss-Jordan elimi- nations (row operations): ± 12 | 3 36 10 | 5 ² subtract 3 times row I From row II ± | 3 00 2 6 |− 4 ² divide row II by 2 ± | 3 00 1 3 2 ² add row II to row I ± 120 1 | 1 001 3 2 ² ±rom the RRE± we see that variables y and w are going to be arbitrary parameters, while x and z are going to be expressed in terms oF these parameters. We successively write: w = s, z =3 s 2 ,y = t, x = 2 t + s +1 , For arbitrary real parameters s and t . We can also write the solution in the Form x y z w = 2 t + s t 3 s 2 s
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