Two subsets

Let $val6 be a vector space. We have two subsets of $val6, and , having respectively $val9 and $val10 elements. Answer:

Two subsets II

Let $val6 be a vector space. We have two subsets of $val6, and , having respectively $val17 and $val18 elements. Answer:

If $val37, is it true that $val40 ?
If $val38, is it true that $val41 ?

Dim matrix antisym

What is the dimension of the (real) vector space composed of real antisymmetric matrices of size $val6×$val6?

Dim matrix sym

What is the dimension of the (real) vector space composed of symmetric real matrices of size $val6×$val6?

Dim matrix triang

What is the dimension of the (real) vector space composed of real $val8 triangular matrices of size $val6×$val6?

Dim poly with roots

What is the dimension of the vector space composed of real polynomials of degree at most $val6, having $val8 as a root of multiplicity at least $val7?

Parametrized vector

Let v1=($val23) and v2=($val24) be two vectors in . Find the value for the parameter t such that the vector v=($val21) belongs to the subspace of generated by v1 and v2.

Shelf of bookshop 3 authors

A bookshop ranges its shelf of novels.

How many titles are there in total for these three authors?


Dim(ker) endomorphism

Let be a vector space of dimension $val6, and an endomorphism. One knows that the image of is of dimension $val7. What is the minimum of the dimension of the kernel of ?

Dim subspace by system

Let E be a sub-vector space of R$val9 defined by a homogeneous linear system. This system is composed of $val7 equations, and the rank of the coefficient matrix of this system is equal to $val6. What is the dimension of E?

Generation and dependency

Let $val6 be a vector space of dimension $val21, and let $val7 be a set of $val25 $val26. Study the truth of the following statements.

$val31.
$val32.
$val33.

Dim intersection of subspaces

Let be a vector space of dimension $val6, and , two subspaces of with , . One supposes that and generate . What is the dimension of the intersection ?

Image of vector 2D

Let be a linear map, with , . Compute , where .$m_par To give your reply, one writes .

Image of vector 2D II

Let be a linear map, with , . Compute , where .$m_par To give your reply, one writes .

Image of vector 3D

Let be a linear map, with , , . Compute , where .$m_par To give your reply, one writes .

Image of vector 3D II

Let be a linear map, with , , . Compute , where .$m_par To give your reply, one writes .