Assignment 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_ The decoded numbers are: 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 decoded message. Decoding using Matrices 7 5 20 0 8 5 12 16

[7 5 ][20 0][8 5][12 16]

Encode use A= Convert: GET HELP A message written according to a secret code.

From the Greek word Kryptos meaning hidden and gramma meaning letter Cryptograms The solution is: (-3,7) !!! Solve the system:

2x+y=1

3x-2y=-23 Example 2- Cramer’s Rule 2x2 Square units = Area= Find the area of the triangle. 8.5 Cont. Using Matrices and Determinants in Real Life Use this matix 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 matrices by the inverse on the right to get the decoded numbers. Decoding using Matrices cont… Assign a number to each letter in the alphabet with out a blank space.

Convert the message to numbers partitioned into 1x2 uncoded 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 Steps to create a cryptogram The answer is: (2,0,1)!!! Z=1 Let’s solve for Z Solve the system:

x+3y-z=1

-2x-6y+z=-3

3x+5y-2z=4 Example 3- Cramer’s Rule 3x3 Solution: (-1,2) So: and The coefficient matrix is: Solve the system:

8x+5y=2

2x-4y=-10 Example 1- Cramer’s Rule 2x2 and Let A be the coefficient matrix

Linear System Coeff Matrix Coeff Det.

ax+by=e

cx+dy=f = A

If detA 0, then the system has exactly one solution: Cramer’s Rule for 2x2 System Square units = Area= Find the area of the triangle. *Where ± is used to produce a positive area!! The area of a triangle with vertices (x1,y1), (x2,y2), and (x3,y3)

Area = Area of a Triangle! The coded message is: 9,11,40,60,11,14,8,4 Encoding Cont… r

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# Using determinants in real life

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