Eroxl's NotesGraph
Subspaces (Practice)

Problem 1

Do the vectors form basis of or .

All the vectors are linearly independent and there are 3 of them each being in so they form a basis for .

Problem 2

Given the following matrix and it's echelon form determine a basis for and .

Problem 3

If is a matrix and is the zero subspace, what can you say about solutions of equations of the form for in ?

The equation has only the trivial solution via the rank theorem.