# Calculus 3 : Matrices

## Example Questions

### Example Question #1 : Matrices

Calculate the determinant of Matrix .

Explanation:

In order to find the determinant of , we first need to copy down the first two columns into columns 4 and 5.

The next step is to multiply the down diagonals.

The next step is to multiply the up diagonals.

The last step is to substract  from .

### Example Question #2 : Matrices

Calculate the determinant of Matrix .

Explanation:

In order to find the determinant of , we first need to copy down the first two columns into columns 4 and 5.

The next step is to multiply the down diagonals.

The next step is to multiply the up diagonals.

The last step is to substract  from .

### Example Question #3 : Matrices

Calculate the determinant of .

Explanation:

All we need to do is multiply the main diagonal and substract it from the off diagonal.

### Example Question #4 : Matrices

Which of the following is a way to represent the computation using matrices?

Explanation:

This choice is the only pair with a well-defined operation; the others are meaningless in terms of matrix multiplication.

Computing this we get

.

Which is the same as

.

This operation is true for (real) -dimensional vectors in general;

### Example Question #5 : 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 #5 : 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 #7 : 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 #8 : 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 #9 : 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 #10 : Matrices

Find the determinant of the matrix