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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