Worked examples

Vector spaces, bases and dimension

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.

• 1Subspace checks with the criterion
• 2Studies of linear dependence and independence
• 3Bases and dimension of subspaces defined by equations
• 4Coordinates of a vector with respect to a basis
• 5Extracting and completing bases
• 6Conversions between parametric form and Cartesian form
• 7Sums and intersections of subspaces with Grassmann's formula