1. Determinants
2 x 2 and 3 x 3 Matrices

2. 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 8 -3

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 2 -¾ 4
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4. 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 2 -¾ 4
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180 4 -¾ 2 8 -3

5. Determinant of a 2x2 matrix1 3 -½

6. 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 2 -¾ 4
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7. 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 2 -¾ 4
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8. 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 2 -¾ 4
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