1 | Show that a set of vectors is a basis for a vector space. |
2 | Find the transition matrix from one basis to another. |
3 | Find a basis for null, row and column space of a matrix. |
4 | Find the rank, nullity, dimension of row and column spaces of a matrix. |
5 | Show that a given formula defines or not an inner product. |
6 | Use the Gram-Schmidt process to constract an orthogonal or orthonormal basis for an inner product space. |
7 | Determine whether a function is a linear transformation. |
8 | Find a basis for the kernel (or range) of a linear transformation. |
9 | Find the eigenvalues and eigenvectors of a matrix. |
10 | Determine whether a given square matrix diagonalizable. |