Warm-up 1. Find A-1 , A = 2. Solve AX = B when B =

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Warm-up 1. Find A-1 , A = 2. Solve AX = B when B =

Table of Contents 27. Matrix Applications

Area of a Triangle! The area of a triangle with vertices (x1,y1), (x2,y2), and (x3,y3) Area = *Where ± is used to produce a positive area!!

Find the area of the triangle. = Square units

You try!! Find the area of the triangle. = Square units

Equation of a line To find the equation of a line passing through points (x1,y1) (x2,y2 )

Example Find the equation of the line through (2,4) and (-1,3).

You try!!! Find the equation of the line through (0,0) and (5,3)

Determining if points are collinear (on the same line) Find out if the determinant of the following matrix is equal to 0. If it is, points are collinear If it is not, points are not collinear

Example Are (-2,-2) (1,1) and (7,5) collinear?

You try!! Are (-3,-5) (6,1) and (10,2) collinear? ?????

Cryptograms A message written according to a secret code. From the Greek word Kryptos meaning hidden and gramma meaning letter

Steps to create a cryptogram Assign a number to each letter in the alphabet with out a blank space. Convert the message to numbers broken up into 1x2 row matrices. To encode a message, choose a 2x2 matrix A that has an inverse and multiply the uncoded row matrices by A on the right to obtain coded row matrices

Convert: GET HELP 7 5 20 0 8 5 12 16 [7 5 ][20 0][8 5][12 16] Encode use A=

Encoding Cont… The coded message is: 9,11,40,60,11,14,8,4

Decoding using Matrices If you don’t know the matrix used to encode - decoding would be very difficult. When a larger coding matrix is used, decoding is even more difficult. But for an authorized receiver who knows the matrix A, decoding is simple. The receiver only needs to multiply the coded row matrices by A-1 on the right to retrieve the uncoded message.

Decoding using Matrices cont… Use to decode: -4,3,-23,12,-26,13,15,-5,31,-5,-38,19, -21,12,20,0,75,-25 First, group the numbers in twos. Find the inverse of the matrix used to code. Then multiply the 1x2 coded martices by the inverse on the right to get the decoded numbers.

The decoded numbers are: 2,5,1,13,0,13,5,0,21,16,0,19,3,15,20,20,25,0 Now use the coded alphabet to translate to: BEAM_ME_UP_SCOTTY_

Assessment Imagine you are the teacher. If you are making a test for matrices, what would you put on it and why? Give 5 examples of problems that would be on you test.