9.7 1) ~v+ 2v~2−5v~1 =~0
~v =−2v~2+ 5v~1
=−2
−1 4
+ 5
−2 3
=
−2·(−1) + 5·(−2)
−2·4 + 5·3
=
−8 7
2) −3~v−v~3 = 12v~3−v~1
−3~v = 32v~3
−v~1
~v =−
1
2v~3+13v~1
=−
1 2
3 4
+ 13
−2 3
=
−
1
2 ·3 + 13 ·(−2)
−
1
2 ·4 + 13 ·3
=
−
13 6
−1
3) 53~v+32v~4 =v~3−2v~2
5
3~v =v~3
−2v~2
−
3 2v~4
~v = 35v~3
−
6 5v~2
−
9 10v~4
= 35 3
4
−
6 5
−1 4
−
9 10
4 0
=
3 5 ·3−
6
5 ·(−1)−
9 10·4
3 5 ·4−
6 5 ·4−
9 10·0
!
= −
3 5
−
12 5
!
Géométrie : bases Corrigé 9.7