# Calculus 3 : Matrices

## Example Questions

### Example Question #11 : 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 #12 : 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 #13 : 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 #14 : 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:

Note that the zero-value determinant means that the two columns are not lineraly independent; one can be found by multiplying the other by some value: in this case, the second column is one half of the first.

### Example Question #15 : 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 #16 : 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 #17 : 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 #18 : 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 #19 : 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 #20 : Matrices

Find the determinant of the matrix