MATA33H3 Lecture Notes - Lecture 11: Triangular Matrix, Main Diagonal
3
MATA33H3 Full Course Notes
Verified Note
3 documents
Document Summary
Properties of determinants (i) the determinant of a 1 by 1 matrix ! a" is a. Let a be an n n matrix. (ii) suppose a de nition is provided for a n 1 by n 1 determinant. If a has a row or column of zeros, det a = 0. If a is a triangular matrix, det a is the product of the elements on the main diagonal. det i = 1. det a = det at . Interchanging any two rows (or columns) multiplies the determi- where aij is the matrix obtained from a by deleting the ith row nant by 1. and jth column. notes: The matrix aij is sometimes called the ij th minor matrix of a. Think of this approach as the de nition by expansion along the rst row or expansion by minors along the rst row.
