Math 54(R) Homework #1 Answer Key
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 =============================  Hill section 1.1  =============================

1-3. NNY

21.
     2 x1 +   x2 + 3 x3 = -6
          - 3 x2 - 2 x3 = -2
                   2 x3 = -4
     (-1, 2, -2)

25.
     3 x1 +   x2 + 2 x3 + 3 x4 =  9
          - 2 x2 +   x3 + 2 x4 =  2
                 - 3 x3 +   x4 = -1
                          2 x4 =  4
     (-1/6, 3/2, 1, 2)

28.
     5 x1 +   x2 + 2 x3 + 3 x4 =  0
            4 x2 -   x3 -   x4 =  0
                   5 x3 + 2 x4 =  0
                        - 3 x4 =  0
     (0, 0, 0, 0)
     Note: this system *is* consistent.

 =============================  Hill section 1.2  =============================

1-6. YNYNNY

 8.  (1/2 t - 5, t, -2), where t is arbitrary

10.  (5/4 t - 3/4 s + 9/2, s, -2 - t, t), where s and t are arbitrary

12.  (2/3 t - 10/3, -3/4 t - 5/2, -1/2 t + 1, t), where t is arbitrary

16.  (0, 0, 0)
     Note: elimination yields the REF system
     [1   7 -7 | 0]
     [0 -11 15 | 0]
     [0   0 -5 | 0]

18.  (3, -t - 1, t), where t is arbitrary
     Note: elimination yields the REF system
     [1 -1 -1 |  4]
     [0  2  2 | -2]