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Determinants . 2 x 2 and 3 x 3 Matrices. 1. 3. -½ . 0. -3. 8. ¼. 2. 0. -¾ . 4. 180. 11. 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.

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Determinants l.jpg

Determinants

2 x 2 and 3 x 3 Matrices


Matrices l.jpg

1

3

0

-3

8

¼

2

0

4

180

11

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


Determinants3 l.jpg

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.



Determinant of a 3x3 matrix l.jpg
Determinant of a 3x3 matrix 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


Determinant of a 3x3 matrix6 l.jpg
Determinant of a 3x3 matrix matrix!

Now keep the first row crossed.

Cross out the second column.

  • Now take the negative of the double-crossed element.

  • And multiply it by the determinant of the remaining 2x2 matrix.

  • Add it to the previous result.


Determinant of a 3x3 matrix7 l.jpg
Determinant of a 3x3 matrix 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.


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