

IntroductionWe consider area of a parallelogram and volume of a parallelepiped
and the notion of determinant in two and three dimensions,
whose magnitudes are these for figures with their column vectors
as edges. We then consider the application of matrices to
describing linear transformations on vectors, and methods
for evaluating determinants. Topics4.1 Area and Volume and the Determinant in Two and Three Dimensions 4.2 Matrices and Transformations on Vectors; the Meaning of 0 Determinant 4.3 Evaluating the Determinant by Gaussian Elimination and by Row or Column Expansion 4.4 The Determinant and the Inverse of a Matrix 