# Calculus 3 : Matrices

## Example Questions

### Example Question #61 : Matrices

Find the matrix product of , where  and  .

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and

The resulting matrix product is then:

### Example Question #62 : Matrices

Find the matrix product of , where  and  .

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and

The resulting matrix product is then:

In this case, A is a special type of matrix known as an identity matrix.

### Example Question #63 : Matrices

Find the matrix product of , where  and  .

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and

The resulting matrix product is then:

### Example Question #64 : Matrices

Find the matrix product of , where  and  .

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and

The resulting matrix product is then:

### Example Question #2661 : Calculus 3

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 #2662 : Calculus 3

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 #2663 : Calculus 3

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 #2664 : Calculus 3

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 #2665 : Calculus 3

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 #2666 : Calculus 3

Find the determinant of the matrix