# Calculus 3 : Matrices

## Example Questions

### Example Question #111 : 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 #112 : 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 #113 : Matrices

Calculate the determinant of .

Explanation:

In order to find the determinant, we need to multiply the main diagonal components and then subtract the off main diagonal components.

### Example Question #114 : Matrices

Find the product of the two matrices:

Where

and

Explanation:

### Example Question #115 : Matrices

Evaluate the following matrix operation:

where

Explanation:

### Example Question #116 : Matrices

Find the determinant of the matrix A:

14

18

-6

28

-24

-6

Explanation:

The determinant of a matrix

is defined as:

Here, that becomes:

### Example Question #117 : Matrices

What is  ?

Explanation:

To find , we write the rows of  as columns.

Hence,

### Example Question #118 : Matrices

What is ?

Explanation:

To find , we write the rows of  as columns.

Hence,

### Example Question #119 : Matrices

Find the determinant of the matrix.

Explanation:

The formula for the determinant of a 3x3 matrix

is

.

Using the matrix we were given, we get

.

### Example Question #120 : Matrices

Perform the matrix operation.