This page outlines exercises on projections onto subspaces, orthogonal complements, and distances to planes in \(\mathbb{R}^n\). It includes tasks such as projecting vectors, identifying bases for ort...This page outlines exercises on projections onto subspaces, orthogonal complements, and distances to planes in \(\mathbb{R}^n\). It includes tasks such as projecting vectors, identifying bases for orthogonal complements, and calculating distances based on linear equations. Key results feature specific projections and descriptions of orthogonal complements, particularly in three-dimensional spaces. The final exercise requires a proof related to the properties of orthogonal complements.
