1)In R^4 build a maximum independent linear subsystem and calculate the
characteristic for the following system of
vectors:(1,0,1,1),(1,2,0,0),(2,2,1,1),(1,-2,2,2),(0,0,0,1).
2)Consider in the real vectorial space R3[x] the subspaces
V and W generated,respectively,by
3x^3+10x^2-5x+5 x^3+5x^2+5 x^3+4x^2-x+3
and
x^3+2x^2-x+5 x^3+4x^2+6 2x^3+2x^2-3x+9
Determine the dimension and one base for the vectorial subspace V+W
3)Consider the linear application phy:R^3->R^^3 defined by
phy(x,y,z)=(x-y+z,x+y+2z)
Determine Ker(phy),Phy(R^3) and Phy^-1(1,-2)
4)Is it (R^2,+,*) a ring?Justfy.
5)Proove for any set A and B that:
A reunion with B except A intersection with B is a subset of A
|
