# Calculus 3 : Matrices

## Example Questions

### Example Question #41 : Matrices

Find the determinant of the matrix

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix

The determinant is thus:

### Example Question #42 : Matrices

Find the determinant of the matrix

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix

The determinant is thus:

### Example Question #43 : Matrices

Find the determinant of the matrix

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix

The determinant is thus:

### Example Question #44 : Matrices

Find the determinant of the matrix

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix

The determinant is thus:

### Example Question #45 : Matrices

Find the determinant of the matrix

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix

The determinant is thus:

### Example Question #46 : Matrices

Find the determinant of the matrix

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix

The determinant is thus:

### Example Question #47 : Matrices

Find the determinant of the matrix

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

For the matrix

The determinant is thus:

### Example Question #48 : Matrices

Find the determinant of the matrix

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

For the matrix

The determinant is thus:

### Example Question #49 : Matrices

Find the determinant of the matrix

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

For the matrix

The determinant is thus:

This result is due to the columns being linearly dependent, i.e. multiples of each other. The first column is three times the second column.

### Example Question #50 : Matrices

Find the determinant of the matrix