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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