[Solution] Practice Midterm #1
YichiZhang204458409
Step 1) The augmented matrix is 2 3 4 1 | 1 1 -3 1 0 | 2 1 0 2 -1 | 8 With Gauss-Jordan elimination, we get 1 0 0 7 | -34 0 1 0 1 | -5 0 0 1 -4 | 21 Step 2) x+7w=-34 y+w=-5 z-4w=21 x=-7w-34 y=-w-5 z=4w+21 Thus for some arbitrary w=t, we have x -7t-34 y = -t-5 z 4t+21 w t Step 4) we can check our answer by substitution 2(-7t-34)+3(-t-5)+4(4t+21)+t=-14t-68-3t-15+16t+84+t=1 1(-7t-34)+(-3)(-t-5)+1(4t+21)+0t=-7t-34+3t+15+4t+21=2 1(-7t-34)+0(-t-5)+2(4t+21)+(-1)t=-7t-34+8t+42-t=8
aleksanderjanczewski: May 5, 2015, 7:28 p.m.
{3, 4}