18.03 Lecture Notes - Lecture 25: Row Echelon Form, Diagonal Matrix, Triangular Matrix
Document Summary
Understanding how to compute the determinant of an arbitrary square matrix using laplace expansion. Understand how the determinant of a matrix geometrically acts as a volume scaling factor. Understand how to invert a square matrix geometrically acts as a volume scaling factor. Understand the conditions for invertibility of a matrix, and how the determinant relates to these conditions. Understand how the invertibility of a matrix relates the space of solutions to the equation ax = b. The absolute value of the determinant of a is the area scaling factor (or the volume scaling factor) The general rule leading to nding the determinant of and n x n matrix when n 3 is as follows: Move your nger along the entries in a row. Remember that the determinant of a is equal to the determinant of the transpose of a. The diagonal of a matrix consists of the entries a with i = j.
