# Calculus 3 : Matrices

## Example Questions

### Example Question #121 : Matrices

Perform the following matrix operation:

Explanation:

To perform the matrix operation, you must follow the formula

.

Using the values we have, this becomes

which simplified is

### Example Question #122 : Matrices

Find the determinant of the 3x3 matrix:

Explanation:

The formula for the determinant is as follows:

,

where

.

Using the matrix in the problem, we get

### Example Question #123 : Matrices

What is  ?

Explanation:

To find

, we write the rows of

as columns.

Hence,

### Example Question #124 : Matrices

Find the determinant of the 3x3 matrix

Explanation:

The formula for the determinant of a 3x3 matrix  is . Using the matrix in the problem statement, we get

### Example Question #125 : Matrices

Evaluate the determinant of the matrix.

Explanation:

The determinant of the  matrix

is defined as

For the matrix in this problem the determinant is

### Example Question #126 : Matrices

Find the determinant of the matrix:

Explanation:

To find the determinant of the matrix, we multiply across, from top left to bottom right, and then subtract the product of multiplying across from top right to bottom left:

### Example Question #127 : Matrices

Find the determinant of the 2x2 matrix

Explanation:

The formula for the determinant of a 2x2 matrix  is . Using the matrix from the problem statement, we get

### Example Question #128 : Matrices

Find the determinant of the 2x2 matrix

Explanation:

The formula foe the determinant of a 2x2 matrix   is . Using the matrix from the problem statement, we get

### Example Question #129 : Matrices

Find the determinant of the given matrix:

Explanation:

The determinant of the matrix is found by multiplying from top left to bottom right, and then subtracting the product from top right to bottom left (for example, the determinant of )