Worked examples

Linear systems and rank

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Linear systems solved with Gaussian elimination
• 2Computing the rank of a matrix
• 3Consistency and number of solutions with the Rouché-Capelli theorem
• 4Systems solved with Cramer's rule
• 5Homogeneous systems and structure of the solutions
• 6Square systems with a parameter
• 7Systems with a parameter that are not square or have a singular matrix