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Determinants 2 x 2 and 3 x 3 Matrices Note that Matrix is the singular form, matrices is the plural form! Matrices 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 1 3 -½ 0 -3 8 ¼ 2 0 -¾ 4 180 11 Note the difference in the matrix and the determinant of the matrix! Determinants 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. 1 3 -½ 0 -3 8 ¼ 2 0 -¾ 4 180 11 Determinant of a 2x2 matrix 1 3 1 0 3 1 -½ 0 2 3 2 Determinant of a 3x3 matrix Imagine crossing out the first row. And the first column. -3 8 ¼ 2 0 -¾ 4 180 11 Now take the double-crossed element. . . And multiply it by the determinant of the remaining 2x2 matrix 3 0 11 3 4 180 Determinant of a 3x3 matrix •Now take the negative of the doublecrossed element. •And multiply it by the determinant of the remaining 2x2 matrix. •Add it to the previous result. Now keep the first row crossed. Cross out the second column. -3 8 ¼ 2 0 -¾ 4 180 11 3 0 11 3 4 180 8 211 3 4 4 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. •Then add it to the previous piece. -3 8 ¼ 2 0 -¾ 4 180 11 4 180 8 211 3 4 4 1 2 180 0 4 695 4 3 0 11 3