Universidade Federal de Vi¸cosa
Centro de Ciˆencias Exatas
Departamento de Matem´atica
Gabarito 1aLista - MAT 137 - Introdu¸c˜ao `a ´
Algebra Linear
2012/I
1. a)N˜ao, b)N˜ao, c)Sim, ordem 4x5, d)N˜ao
2. a)A5×6, b)B3×6, c) C3×4, d) D4×3, e)E3×5
3. a)A4×5, b)a23 = 11, a35 = 3, a43 =−4.
4. A3×2,B2×3,C3×2,D2×3,E3×2
5. c32 = 18, d43 = 23.
6. A=
3−4−7−10
−2 8 −5−8
−5−1 15 −6
−8−4 0 24
7. a)A2=I, b)A3=A, c)A31 =A, d)A42 =I
8. x=−1, y = 1
9. a)x= 4,b)x= 12, y =−8, z =−4,c) x= 2, y =−7, z =−2
x=−2, y =−3, z = 10
10. a)
22 −6 8
−246
10 0 4
,b)[724
357],c)A=
9−13 0
1 2 1
−1−4−6
,d)
10 −6
−14 2
−6−8
11. a)[1 1
1 1 ],[−1−1
−1−1]
b)4 matrizes: [√5 0
0 3 ],[−√5 0
0 3 ],[√5 0
0−3],[−√5 0
0−3]
c) N˜ao, A=[−1 0
0−1]
12.
13.
14. a)±1,b) [0 1
−1 0 ]e[0−1
1 0 ]
15. m=±1
1
