# Maddie's Matrices Lesson

### By: Maddie McGuire

## What are Matrices??

A Matrix can be defined as a rectangular array of numbers. symbols or expressions which are arranged into rows and columns. Matrices are used to be interpreted in many different ways and can undergo the four basic operations of algebra; addition, subtraction, multiplication, and division.

## Adding Matrices!

## Step 1 Write down both matrices given in a problem on your paper and make sure all number are copied correctly and labeled correctly. | ## Step 2 Add the numbers that are in the same position as one another. For example, 3 and 4 will be added together because they are both in the lower left hand corner of the matrix. | ## Step 3 Once all the addition of the four positions are done, a new matrix labeled [A+B] will be made. Simplify if needed. |

## Step 1

Write down both matrices given in a problem on your paper and make sure all number are copied correctly and labeled correctly.

## Step 2

Add the numbers that are in the same position as one another. For example, 3 and 4 will be added together because they are both in the lower left hand corner of the matrix.

## Subtracting Matrices!

## Step 1 The same approach will be taken as above in adding matrices. Copy all matrices down that are going to be used in the problem and check that all numbers and labeling are correct. | ## Step 2 Subtract the numbers that are in the same position as one another. For example, 3 and 4 can be subtracted together because both are in the lower left hand corner of the matrix. | ## Step 3 Once all the subtraction of the four positions are done, a new matrix labeled [A-B] will be made. Simplify if needed. |

## Step 1

The same approach will be taken as above in adding matrices. Copy all matrices down that are going to be used in the problem and check that all numbers and labeling are correct.

## Step 2

Subtract the numbers that are in the same position as one another. For example, 3 and 4 can be subtracted together because both are in the lower left hand corner of the matrix.

## Multiplying Matrices!

## Step 1 Copy down matrices given in the problem and make sure that the number of columns in Matrix A is equal to the number rows in Matrix B. | ## Step 2 Multiply the first row in Matrix A by the first column in Matrix B, this number corresponds with top left corner position. Then, multiply the first row again in Matrix A by the second column in Matrix B, this corresponds with the top right position. Complete these two parts again for the second row in Matrix A, and put the numbers in their corresponding positions. | ## Step 3 Simplify all numbers to get the final Matrix labeled [AB}. |

## Step 1

Copy down matrices given in the problem and make sure that the number of columns in Matrix A is equal to the number rows in Matrix B.

## Step 2

Multiply the first row in Matrix A by the first column in Matrix B, this number corresponds with top left corner position. Then, multiply the first row again in Matrix A by the second column in Matrix B, this corresponds with the top right position. Complete these two parts again for the second row in Matrix A, and put the numbers in their corresponding positions.

## Determinants!

## Step 1 Copy down the matrix in the given problem. | ## Step 2 Multiply the two diagonals in the matrix. | ## Step 3 Subtract the two values that you got from multiplying the diagonals, and that will be your determinant. |

The second way to find the determinant is with a 3 by 3 matrix, called the third order determinant.

## Step 1 Copy down the Matrix given for the problem and then rewrite the first two columns to the right of the Matrix. | ## Step 2 Staring with the first number in the top left corner and draw a diagonal to the number in bottom right corner. Do this three times until the whole first row is apart of a diagonal. Multiply all three numbers in each diagonal together and then add those products. Repeat these steps, but starting with the top right corner box. Again, multiply the three numbers together and then add those products. | ## Step 3 Simplify the problem by subtracting the sum of the second set of diagonal's products by the first set of diagonal's products. |

## Step 1

Copy down the Matrix given for the problem and then rewrite the first two columns to the right of the Matrix.

## Step 2

Staring with the first number in the top left corner and draw a diagonal to the number in bottom right corner. Do this three times until the whole first row is apart of a diagonal. Multiply all three numbers in each diagonal together and then add those products. Repeat these steps, but starting with the top right corner box. Again, multiply the three numbers together and then add those products.

## Upcoming Assessments:

**Quiz 4 -**December 8th

**Test 2 - **December 10th

## Citations

-Accelerated Algebra II textbook

- http://www.mathsisfun.com/algebra/matrix-introduction.html