Explained why det(AB) = det(A) det(B) for 2×2 matrices A, B. Then proved that the determinant of a 2×2 matrix is +/- the area of a certain parallelogram.
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Introduced the definition of an eigenvector of a matrix A with associated eigenvalue. Gave some examples of eigenvectors and eigenvalues.
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Noted that the matrix A of rotation about the origin through an angle (not equal to 0 or 180 degrees) has no eigenvectors.