MATH125 Lecture Notes - Lecture 10: Triangular Matrix, Null Character, Linear Independence

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Vladimir Chernousov

Document Summary

Definition: the scalar is called the determinant or our matrix of arbitrary size. In a 3x3 matrix, a simple way to find the determinant is to do the positive and negative diagonals" method. Where you add up the products of the positive" lines and subtract the products of the negative" lines you are given the determinant . There is another method of finding the determinant,: Definition: aij is a matrix obtained from deleting the ith row and the jth column, its determinant is called the i,j minor of a. Definition: let a be a matrix of size nxn, then the determinant of a is the following scalar: deta=a11deta11-a12deta12+a13deta13-+(-1)^na1ndeta1n. The determinant is not defined if the matrix is not square. Definition: the scalar (-1)^i+jaij is called the cofactor of submatrix aij, with notation cij. This is the +, -, +, - system. Therefore the determinant is actually defined as deta=a11c11+a12c12+a13c13+a1nc1n. This formula is called expansion across the first row.