- Geometric meaning of a system of linear equations,
- A reduction of the matrix of Ax=b to the echelon form by Gaussian elimination
and backward substitution,

- a sage worksheet - An example for the proof of rank uniqueness,
- Solving a non-homogeneous system
- Ill-conditioned system
- Matrix product
- Associativity of the matrix product
- Elementary transformations as matrix products

- a sage worksheet - Matrix inversion

- a sage worksheet - Matrix equations

- a sage worksheet based on this exercise from the collection - Group S3 and some if its subgroups
- Residue classes as a quotient group
- The field Z7
- The field GF(4)
- An example of a solution of a system Ax=b over Z7
- An inverse matrix over Z5
- Lagrange interpolation
- Real functions as a vector space over R
- Set systems as vector spaces over Z2
- Intersection of subspaces is a subspace
- A linear hull
- Two tests of linear independence
- Distinct ways to describe a vector space
- Coordinates of a vector w.r.t. different bases
- The exchange lemma - an example in R^3
- The exchange theorem - an example in V=Z2^4
- The dimensions of the row and of the column spaces are equal
- Examples of linear maps
- The matrix of a map in the plane
- The change of basis matrix
- Example of an isomorphism