Vector spaces I - UNSA MI 2001
basis, subspaces, dimension, linear maps, image, kernel.
90 2001
3
U1, U2
algebra, linear algebra
matrix, rank, vector, linear system, basis change, inverse image


This is the translation of a sheet designed for first year students of mathematics and computer science at Université de Nice - Sophia Antipolis, of year 2000-2001.  Each student has had 1h30 to work on this sheet.

:U1/algebra/basechange.en
dim=2
20
1
Compute coordinates
write a vector under a new basis.
:U1/algebra/basechange.en
dim=4
20
2
Compute coordinates II
write a vector under a new basis.
:U1/algebra/genspace.en
x=3&steps=1
30
1
System of vectors and matrix ranks
does a given set of vectors generate the whole vector space?
:U1/algebra/basechoice.en
givtype=sys&gettype=vec&level=3
30
1
Basis choice
find a basis of a vector subspace among given vectors.
:U1/algebra/bases.en
exo=defsys&qnum=1&qcmlevel=3
20
1
Subspace of a system
Find a basis of a vector subspace defined in various ways.
:U1/algebra/linimg.en
map=linear&dim1=2&dim2=3&orient=0
10
1
Linear image I
Compute the image of a vector by a linear map.
:U1/algebra/linimg.en
map=linear&dim1=3&dim2=4&orient=0
10
2
Linear image II
Compute the image of a vector by a linear map.
:U1/algebra/bases.en
exo=kerV&qnum=2&qcmlevel=1
10
1
Compute kernel I
find a basis of the kernel of a linear map.
:U1/algebra/bases.en
exo=kerV&qnum=2&qcmlevel=3
10
1
Compute kernel I
find a basis of the kernel of a linear map.
