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### Rule for multiplying matrices

NOTES 3.3

Flip

Vocab

- TSW
- Identify matrix terminology
- Add Matrices
- Subtract Matrices
- Multiply Matrices
- Enter matrix in a calculator

A matrix is described by its dimensions: rows X columns

Flip

Vocab

one

one

equal

Matrices are used to organize data and solve systems of equations.

zero

element

dimensions

corresponding

A row matrix has _____ row.

A column matrix has _____ column

A square matrix has ________

number of rows and columns

A zero matrix has each

___________ as a _________

Equal matrices have the same

__________ and each element of

one matrix is equal to the

____________element of the

other matrix.

Vocab

A matrix is usually named using a capital letter.element

The dimensions of matrix A are ____ X ____

2 3

4

9

dimensions

Each value in a matrix is called an ___________

Find element A12 = ______

Find element A23 = ______

Matrices can only be added or subtracted if they have the same _______________

Set corresponding locations equal !

x+3y = -13

3x+y = 1

y = -3

Solve the system!

2x+(-3)=5

x = 4

Distribute!

Add to isolate matrix X

Teachers might want to show how calc can add matrices!!

Pick columns

Product matrix will be outer #s: 1 x 2

Pick rows

1

3

3

2

Dimensions: A = ___x___ B=___x___

AB = ___x___

1

2

Inner #s must be same to multiply

Multiply matrices: Find AB

C2

C1

R1

Also show mult on calc.!

Commutative property AB=BA

If the number of columns in the first matrix is not equal to the number of rows in the 2nd matrix, then the product of the two matrices is not defined, or

“Does not Exist” or “DNE”

This property is not always true for matrices.

If A= 2x3 and B= 3x4

You can find AB …..but not BA

Set matching locations equal and solve for w and z

2x2 times 2x2 Product matrix will be a 2 x 2

Columns

Rows

C1

C2

R1

(-3)(4)+(-2)(-5)

(-3)(w)+(-2)(1)

R2

(0)(w)+(6)(1)

(0)(4)+(6)(-5)

Z = -30

w = 7

Convert the matrix to equations and solve the system.

2x2 times 2x1 Product matrix will be a 2 x 1

Set matching locations equal

-3x+2y = 7

-5x+6y = 17

C1

-3x+2y

R1

-5x+6y

R2

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