Page 341 - 35Linear Algebra
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                                                                Sample Final Exam






                   Here are some worked problems typical for what you might expect on a final
                   examination.

                      1. Define the following terms:

                          (a) An orthogonal matrix.
                          (b) A basis for a vector space.
                          (c) The span of a set of vectors.

                          (d) The dimension of a vector space.
                          (e) An eigenvector.
                          (f) A subspace of a vector space.
                          (g) The kernel of a linear transformation.

                          (h) The nullity of a linear transformation.
                          (i) The image of a linear transformation.
                          (j) The rank of a linear transformation.

                          (k) The characteristic polynomial of a square matrix.
                          (l) An equivalence relation.
                         (m) A homogeneous solution to a linear system of equations.
                          (n) A particular solution to a linear system of equations.

                          (o) The general solution to a linear system of equations.
                          (p) The direct sum of a pair of subspaces of a vector space.


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