Curated OER
Linear Systems
In this multiplication of vectors activity, students prove that the dot product operation is commutative. They normalize a vector so it has the same direction with a magnitude of one. Students use the angle formula to confirm orthogonality.
Curated OER
Linear Systems: Vector Spaces of a Matrix
In this vector space matrix worksheet, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page worksheet contains examples and approximately five problems.
Curated OER
Linear Systems: Orthogonality of Subspaces
In this subspace worksheet, students decompose a vector into two orthogonal pieces, one for the nullspace and another for the row space of a matrix. This two-page worksheet contains explanations, examples, and three problems.