Write down the augmented matrix
A=⎝⎛1322−11−3501−11∣∣∣000⎠⎞ R2=R2−3R1
⎝⎛1022−71−31401−41∣∣∣000⎠⎞ R3=R3−2R1
⎝⎛1002−7−3−31461−4−1∣∣∣000⎠⎞ R2=−R2/7
⎝⎛10021−3−3−2614/7−1∣∣∣000⎠⎞ R1=R1−2R2
⎝⎛10001−31−26−1/74/7−1∣∣∣000⎠⎞ R3=R3+3R2
⎝⎛1000101−20−1/74/75/7∣∣∣000⎠⎞R3=7R3/5
⎝⎛1000101−20−1/74/71∣∣∣000⎠⎞
R1=R1+R3/7
⎝⎛1000101−2004/71∣∣∣000⎠⎞ R2=R2−4R3/7
⎝⎛1000101−20001∣∣∣000⎠⎞Take x3=t,t∈R.
Then x1=−t,x2=2t,x3=t,x4=0,t∈R
{−t,2t,t,0},t∈R
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