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Vector spaces I - UNSA MP 2001
basis, subspaces, dimension, linear maps, image, kernel.
180 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 physics at Université de Nice - Sophia Antipolis, of year 2000-2001.  Each student has had 3 hours to work on this sheet.

:U1/algebra/basechange.en
dim=2
30
1
Compute coordinates I
write a vector under a new basis.
:U1/algebra/basechange.en
dim=4
20
1
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/bases.en
exo=defsys&qnum=1&qcmlevel=3
30
1
Bases I
Find a basis of a vector subspace defined in various ways.
:U1/algebra/bases.en
exo=defsys&qnum=1&qcmlevel=5
20
1
Bases II
Find a basis of a vector subspace defined in various ways.
:U1/algebra/linimg.en
map=linear&dim1=3&dim2=3&orient=0
20
1
Linear image
Compute the image of a vector by a linear map.
:U1/algebra/linimg.en
map=linear&dim1=3&dim2=3&orient=1
20
1
Linear inverse
determine a vector whose image by a linear map is given.
:U1/algebra/basechoice.en
givtype=sys&gettype=vec&level=5
30
1
Basis choice
find a basis of a vector subspace among given vectors.
:U1/algebra/oefvecspa.en
exo=intsdim&exo=dimkercomp&exo=Dimmatriceanti&exo=Dimmatricesym&exo=Dimmatricetria&exo=dimsev&exo=linim2d2&exo=linim2d&exo=linim3d2&exo=linim3d&qnum=3&qcmlevel=3
20
2
Vector spaces
exercises on vector spaces