__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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