THU, JAN 8, 2015

Create a “Big Book of Matrices” flip book using 4 pages.Do not make your tabs big!

BIG BOOK OF MATRICES• What is a Matrix?

• Adding & Subtracting• Multiply by a Scalar

• Multiplication• Solve Systems using RREF• Finding an Inverse Matrix

• Solve Systems using Inverses

MATRICES

What is a Matrix?• A matrix is an array of numbers written in rows and columns.• The dimension indicates how may rows and columns it has (rows first,

columns second).• Matrix is singular, Matrices is plural

2x3 3x2 3x1 2x2

• A Square Matrix has the same number of Rows and Columns.

[3 −2 10 4 5] [−2 1

4 10 −1] [ 1−93 ] [1 −8

2 −3]

Adding & Subtracting• In order to add or subtract matrices the dimension must be the same.• If the dimensions are not the same…cannot be added or subtracted!

[3 24 −1]+[1 −2

5 0 ]=¿[4 09 −1]

NO SOLUTION

[0 81 42 −2]−[−1 −1

3 50 −4 ]=¿[ 1 9

−2 −12 2 ]

=

Scalar Multiplication• A Scalar is just a number you are multiplying by, or distributing.

4 [3 02 −1]=¿[12 0

8 −4 ]

−3 [ 4−12 ]+2[135 ]=¿[−123−6 ]+[ 2610 ]=¿ [−1094 ]4 [ 0 1−3 2]+3 [3 −1 ]=¿[ 0 4

−12 8 ]+ [9 −3 ]

Multiplication• Only compatible matrices can be multiplied.• Compatible: 2x3 • 3x1 2x1 • 1x6 3x2 • 2x2 3x3 • 3x3• NOT Compatible: 2x3 • 2x3 2x2 • 3x2 1x2 • 3x1

2x3 • 3x1 = 2x1

[2 1 30 2 4 ] ∙[123]= [¿ ]

2x2 • 2x3 = 2x3

2x1 • 2x2 = Not Compatible

NO SOLUTION

=

Please see video under Recommended Resources to

help you go through the process of multiplication.

Solving Systems using RREF• RREF is Reduced Row Echelon Form• AKA Gauss-Jordan Elimination• Use for a system of Linear Equations!

Solve the system algebraically using Reduced Row Echelon Form: x + y = -1 2x – 3y = 13

Solve the system using the calculator:

• Go to MATRIX, then EDIT.• Type in the dimension (this is a 2x3)• Type in the numbers• Go to MATRIX, then MATH• Find RREF (don’t forget to tell the calculator what matrix to RREF!)

Please see video under Recommended Resources to help you

solve systems using row reducing

Finding the Inverse of a Matrix• Only Square Matrices can have Inverses• Not ALL Square Matrices have Inverses, some are undefined (If the

Determinant = 0, NO INVERSE)• If you have Matrix A, the Inverse of Matrix A is denoted by A-1

Find the inverse:

[2 17 4 ]

Use your calculator to find the Inverse of each Matrix:

A-1 = B-1 = C-1 =

A = B =

C =

Please see video under Recommended Resources to help you

find an inverse of a matrix.

Solve Systems using Inverses• The A Matrix contains the coefficients, the X Matrix contains the variables and the

B Matrix contains what the equations equal: AX = B• When solving, you cannot divide by Matrix A, you MUST use the Inverse, so: X = A-1B A • X = B X = A-1 • B x + y = -1 2x – 3y = 13 [1 1

2 −3] ∙[ 𝑥𝑦 ]=[−113 ] [𝑥𝑦 ]=[ 35 15

25

−15

] ∙[−113 ] [𝑥𝑦 ]=[ 2−3 ]

Solve each system on the calculator using Inverse Matrices.

• Type in the A Matrix and the B Matrix• Find A-1B