1016-331 RIT, 20091 1
Linear Algebra I 1016-331
Quiz 4 Solution
1. Find the inverse of the given matrix (if it exists).
A=·4 7
1 2 ¸
We compute
A=·4710
1201¸R1↔R2
;·1 2 0 1
4 7 1 0 ¸R2−4R1
;·1 2 0 1
0−1 1 −4¸−R2
;
·1 2 0 1
0 1 −1 4 ¸R1−2R2
;·1 0 2 −7
0 1 −1 4 ¸.
So the inverse is
A−1=·2−7
−1 4 ¸.
2. Find the inverse of the given matrix (if it exists).
F=
1 0 0
a1 0
a2a1
.
We compute
F=
1 0 0 1 0 0
a1 0 0 1 0
a2a1 0 0 1
R2−aR1,R3−a2R1
;
1 0 0 1 0 0
0 1 0 −a1 0
0a1−a20 1
R3−aR2
;
1 0 0 1 0 0
010−a1 0
0 0 1 0 −a1
.
So the inverse is
A−1=
1 0 0
−a1 0
0−a1
.