It will be important to compute the set of all vectors that are orthogonal to a given set of vectors. It turns out that a vector is orthogonal to a set of vectors if and only if it is orthogonal to th...It will be important to compute the set of all vectors that are orthogonal to a given set of vectors. It turns out that a vector is orthogonal to a set of vectors if and only if it is orthogonal to the span of those vectors, which is a subspace, so we restrict ourselves to the case of subspaces.
This page presents exercises on matrices, emphasizing the calculation of bases for row, column, and null spaces, alongside ranks and nullities. It validates the Rank-Nullity Theorem and explores kerne...This page presents exercises on matrices, emphasizing the calculation of bases for row, column, and null spaces, alongside ranks and nullities. It validates the Rank-Nullity Theorem and explores kernel spaces as subspaces of \( \mathbb{R}^n \). Key topics include linearly independent rows, pivot columns, and methods for solving linear algebra problems.
