Determinants 2 x 2 and 3 x 3 Matrices

Matrices Note that Matrix is the singular form, matrices is the plural form! A matrix is an array of numbers that are arranged in rows and columns. A matrix is “square” if it has the same number of rows as columns. We will consider only 2x2 and 3x3 square matrices -½ 3 1 11 180 4 -¾ 2 ¼ 8 -3

Determinants 1 3 -½ Every square matrix has a determinant. Every square matrix has a determinant. The determinant of a matrix is a number. We will consider the determinants only of 2x2 and 3x3 matrices. -3 8 ¼ 2 -¾ 4 180 11

Notation -½ 3 1 1 3 -½ -3 8 ¼ 2 -¾ 4 180 11 11 180 4 -¾ 2 ¼ 8 -3 Note the difference in the matrix and the determinant of the matrix! -½ 3 1 1 3 -½ Determinants---these are numbers! Matrices—arrays of numbers -3 8 ¼ 2 -¾ 4 180 11 11 180 4 -¾ 2 ¼ 8 -3

Determinant of a 2x2 matrix 1 3 -½

Determinant of a 3x3 matrix Imagine crossing out the first row. And the first column. Now take the double-crossed element. . . And multiply it by the determinant of the remaining 2x2 matrix -3 8 ¼ 2 -¾ 4 180 11

Determinant of a 3x3 matrix Now keep the first row crossed. Cross out the second column. Add the negative of the double-crossed element. . . . . .multiplied by the determinant of the remaining 2x2 matrix. -3 8 ¼ 2 -¾ 4 180 11

Determinant of a 3x3 matrix Finally, cross out first row and last column. Now take the double-crossed element.. . . . multiply it by the determinant of the remaining 2x2 matrix . . . . . .and add it to the previous expression. -3 8 ¼ 2 -¾ 4 180 11