Reduce a matrix


         Find the determinant and inverse of a matrix


         Find all solutions of a system of linear equations, and if there are infinitely many,

write them as a parametrically described set of solutions.


         Determine if a specific vector is in the span of a given set, and if it is,

write it as a linear combination of those vectors


         Describe which vectors can be expressed as a linear combination of a given set of vectors

Describe which vectors are in the span of a given set of vectors (same thing)


         Determine if a given set of vectors is dependent, and if it is, write one of them

as a linear combination of the others


         Use the contraction process to reduce a set that spans a given subspace to a

basis for that subspace


         Use the expansion process to enlarge an independent set of vectors into a basis


         Find the coordinates of a vector relative to a given basis


         Find the inner product of two vectors and the norm of a vector


         Find the angle between two vectors


         Write a vector as the sum of one vector in a given direction and a second vector orthogonal to the given direction


         Gram-Schmidt Orthonormalization


         Computations involving linear transformations


         Computations involving the matrix of a linear transformation (including matrix, kernel, image)


         Find a basis for the row space and column space of a matrix


         Determine whether or linear transformation is one-to-one or whether it is onto



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