1016-331 RIT, 20091 1
Linear Algebra I 1016-331
Quiz 2 Solution
1. Write down the augmented matrix of the system, then use Gauss elimination to find the row
echelon form. State the complete solution of the system.
x+ 2y−z+ 2w= 1
2x−y+ 3z+ 2w= 0
3x+y+ 2z+ 4w= 2.
1 2 −121
2−1 3 2 0
3 1 2 4 2
R2−2R1,R3−3R1
;
1 2 −1 2 1
0−5 5 −2−2
0−5 5 −2−1
R3−R2
;
1 2 −1 2 1
0−5 5 −2−2
0 0 0 0 1
We have a pivot in the last column of the augmented matrix of the system, so it is inconsistent,
there is no solution .
2. Find the rank of the following matrix.
A=
0 2 0 1
0 1 1 0
0 4 0 2
.
We compute:
0201
0110
0402
R2−R1/2,R3−2R1
;
0 2 0 1
0 0 1 −1/2
0 0 0 0
.
So the rank is 2.