SOME COMPUTATIONS YOU SHOULD BE ABLE TO DO

· 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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