3 LISTA DE EXERC´
ICIOS- ´
ALGEBRA LINEAR I
1. Calcule o determinantes usando as invers˜oes.
a)
2−1
3 2
b)
0 3 0
2 0 0
0 0 −5
c)
420
0−2 5
003
d)
4 2 2 0
2 0 0 0
3 0 0 1
0 0 1 0
2. Se |A|=
a1a2a3
b1b2b3
c1c2c3
=−4.
Encontre os determinantes das seguintes matrizes
B=
a3a2a1
b3b2b1
c3c2c1
, C =
a1a2a3
b1b2b3
2c12c22c3
e
D=
a1a2a3
b1+ 4c1b2+ 4c2b3+ 4c3
2c12c22c3
3. Se A=
1−1 2
341
251
, verifique se det A =det At.
4. Calcule os determinantes usando o que achar mais conveniente (in-
vers˜oes, Sarrus ou cofatores).
a)
4 6
7 2
c)
1 2 3
−1 5 2
3 2 0
e)
0 1 −2
−1 3 1
2−2 3
g)
−4−4 2 1
1 2 0 3
2 0 3 4
0−3 2 1
b)
−1 2
5 6
d)
4−2 0
024
−1−1−3
f)
2 1 −3
012
−4 2 1
h)
2 2 −3 1
0 1 2 −1
3−1 4 1
2 3 0 0
i)
312−1
203−7
134−5
0−1 1 −5
k)
123−3 1
04000
01011
0−6 6 1 3
020−1 1
j)
0 0 −1 3
0 1 2 1
2−252
3 3 0 0
l)
2 1 5 −1 6
1 4 0 3 7
1 0 0 −7 9
3 2 1 0 8
1 1 0 3 4