The document outlines the significance of linear algebra in computer science, including its applications in graph theory, network models, cryptography, and computer graphics. Linear algebra simplifies complex problems into manageable matrix forms, which are crucial for various scientific fields. The text concludes by emphasizing the diverse applications of linear algebra, ranging from circuit analysis to advanced algorithms.

1. APPLICATIONS OF
LINEAR ALGEBRA IN
COMPUTER SCIENCES
Hafiz Muhammad Amir Sharif
SP12-BSCS-B7(B)-110

2. Objectives
Importance of Linear Algebra
Graph Theory
Network Models
Cryptography
Computer Graphics

3. Why Linear Algebra is important ?
• Linear algebra is vital in multiple areas of science in
general. Because linear equations are so easy to solve,
practically every area of modern science.
• It converts large number of problems to matrix and thus
we solve the matrix.

4. Graph Theory

5. Network Models
• Determine the currents I1, I2, and I3 for the following
electrical network:

6. By Kirchhoff’s Law

7. Cryptography
• Encryption and decryption require the use of some secret
information, usually referred to as a key.
• Example Let the message be
“PREPARE TO NEGOTIATE”
• We assign a number for each letter of the alphabet.

8. Thus the message becomes:
• Since we are using a 3 by 3 matrix, we break the enumerated
message above into a sequence of 3 by 1 vectors:

9. By multiplying encoding matrix to this
matrix we will encrypt the msg

10. Now to decrypt the msg we have to multiply this
matrix to Inverse of encoding matrix
• The inverse of this encoding matrix, the decoding matrix,
is:
• Multiplying again by this matrix we will get our Msg.

11. Computer Graphics
• In computer graphics every element is represented by a
MATRIX.

12. Conclusion:
• There are so many application of Linear Algebra in
Computer Science.
• From simple circuit solving to large web engine
algorithms.

13. Thank you