Application of matrix

1. Application of Matrices
Presented By:
S.DIVIYASRI

2. Matrix
▪ A matrix is a rectangular arrangement of ‘mn’ elements.
▪ It consists of rows and columns arrangements.
▪ It is a systematic arrangement of elements and may represent
vectorial or scalar quantity.

3. Some of the applications of Matrix
▪ Engineering forces on a bridge or truss
▪ Electronics
▪ Genetics (working out selection process)
▪ Probability (finding quantities in a chemical reaction)
▪ Chemistry
▪ Economics (study of stock market, etc)
▪ EncryptionAnd decryption messages –
Cryptography
(here we will discussCryptography)

4. Encryption and Decryption (Cryptography)
▪ A cryptogram is a message written according to a secret code (theGreek word kryptos
means “hidden”).The following describes a method of using matrix multiplication to encode
and decode messages.
▪Then convert the message to numbers and partition it into
encoded row matrices, each having entries
▪In the following example we take an example to
encode the Message “MEET ME MONDAY”

5. Encoding Process
▪ Partitioning the message (including blank spaces, but ignoring punctuation) into groups of
three produces the following uncoded row matrices.
▪ To encode a message, choose an invertible matrix and multiply the uncoded row matrices
(on the right) by to obtain coded row matrices.This inverted matrix will act as a password.
▪ For example here.

6. Encoding Process

7. Encoding Process
▪ The sequence of coded row matrices is
▪ Finally, removing the matrix notation produces the following cryptogram
▪ For those who do not know the encoding matrixA, decoding the cryptogram is possible.
▪ But for an authorized receiver who knows the encoding matrix decoding is relatively simple.
The receiver just needs to multiply the coded row matrices by A-1to retrieve the uncoded row
matrices. In other words, if
▪ is an uncoded 1×n matrix, then Y=XA is the corresponding encoded matrix.The receiver of
the encoded matrix can decode by Y multiplying on the right by A-1.

8. Decoding Process
▪ Begin by usingGauss-Jordan elimination to find A-1
▪ Now, to decode the message, partition the message into groups of three to form the coded
row matrices
▪ To obtain the decoded row matrices, multiply each coded row matrix by A-1

9. Decoding Process

10. Decoding Process
▪ The sequence of decoded row matrices is
▪ And the message is
▪ And the authorized person can easily decode the encoded message using the inverse of the
matrixA, which was the password during encoding.

11. BY
DIVIYASRI.S