Vector spaces II - 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/extsspace.en
dim_total=4&dim_sub1=2&dim_sub2=3&vecs2add=2
10
0.7
Extend-subspace I
extend a vector subspace to a required dimension.
:U1/algebra/extsspace.en
dim_total=5&dim_sub1=3&dim_sub2=4&vecs2add=3
20
1
Extend-subspace II
extend a vector subspace to a required dimension.
:U1/algebra/vecshoot.en
vectors=2&range=1&shoots=2&grid=6
30
0.5
Vector shoot I
click on a linear combination of 2D vectors.
:U1/algebra/vecshoot.en
vectors=2&range=2&shoots=3&grid=3
20
1
Vector shoot II
click on a linear combination of 2D vectors.
:U1/algebra/linshoot.en
type=fix&mat=simple&range=1&shoots=3&grid=3
20
0.5
Linear shoot I
click on the image of a point by a linear transformation. 
:U1/algebra/linshoot.en
type=variable&mat=simple&range=3&shoots=3&grid=0
20
1
Linear shoot II
click on the image of a point by a linear transformation. 
:U1/algebra/coinxform.en
hardness=2&ntry=10&nshape=0&size=200&grid=2
20
1.5
Coincidence Transformation (rotation)
transform a given 2D shape into another given one.
:U1/algebra/coinxform.en
hardness=3&ntry=10&nshape=0&size=200&grid=5
30
1.7
Coincidence linear transform (general linear)
transform a given 2D shape into another given one.
:U1/algebra/oefvecspadef.en
exo=alternate&exo=Espacedapplica&exo=matrices&exo=muldiv&exo=nonnuls&exo=absolu&qnum=3&qcmlevel=3
20
1
Definition of vector space
whether a given set is a vector space.
:U1/algebra/oefsubspadef.en
qnum=4&qcmlevel=3
20
1
Definition of vector subspace
whether a given subset is a vector subspace.
