Algèbre linéaire I Série 8

VKW V
V/W V/W dim V/W = dim V−dim W
W V
x1−x2−2x3−x4= 0
x1+x2−x3−x4+x5= 0
4x1+ 2x2−6x3−3x4+ 3x5= 0
2x1+ 2x2−2x3−x4+ 2x5= 0
a∈C
2x1+ 4a x2−x3= 2
4a x1+ 2x2−2x3= 3
−x1+x2+x3=−1
a, b ∈R
x1−4ax2−x3= 4 + b
−x1+2x2+x3= 8
3ax1+x2+x3=−16 −b
x1, x2, x3∈Rx1< x2< x3y1, y2, y3∈R
p∈R[x]2p(xi) = yi
i= 1,...,3
x1= 0 x2=−2x3= 3 y1= 1 y2= 2 y3= 3
p(x)∈R[x]3p(xi) = yii= 1,...,3
p(x) (1, x, x2, x3)R[x]3