Daffodil Internartional University

1. WELCOME

2. Presentation by:
1. Al-Amin Prince,
ID: 141-19-1539
2. Nusrat Jahan
ID: 141-19-1542
Department of ETE
Daffodil International University.
Guided By:
Md. Mosfiqur Rahman
Senior Lecturer,
Department of General Educational Development
Faculty of Science and Information Technology.

3. Presentation on Application of
Linear Algebra in ETE

4. What is Linear Algebra?
Linear Algebra is the branch of mathematics concerning vector spaces and
linear mappings between such spaces. It includes the study of lines, planes,
and subspaces, but is also concerned with properties common to all vector
spaces.
Hence, the above definition confirms that Linear Algebra is an integral part
of mathematics.

5. Applications of Linear Algebra in various fields
Abstract Thinking
Chemistry
Coding Theory
Cryptography
Economics
Elimination Theory
Games
Genetics
Geometry
Graph Theory
Heat Distribution
Image Compression
Linear Programming
Markov Chains
Networking
Sociology
The Fibonacci Numbers
Eigenfaces

6. LINEAR ALGEBRA
• Linear Algebra most apparently uses by electrical engineers.
• When ever there is system of linear equation arises the concept of
linear algebra.
• Various electrical circuits solution like Kirchhoff's law , Ohm’s law are
conceptually arise linear algebra.
• To solve various linear equations we need to introduce the concept of
linear algebra.
• Using Gaussian Elimination not only computer engineers but most of
daily computational work minimized .
• Now we don’t have to use extremely large number of pages to
calculate complex system of linear equations.

7. GAUSSIAN ELIMINATION
To fix all the assertion that we have performed earlier we use Gaussian
elimination.
In this method we need to keep all eqs. into matrix form, for e.g.
Since the columns are of same variable it’s easy to do row operation
to solve for the unknowns.

8. This method is known as Gaussian Elimination. Now, for large
circuits, this will still be a long process to row reduce to echelonform.
With the help of a computer and the right software , the large circuits
consisting of hundreds of thousands of components can be analyzed in a
relatively short span of time.
Today’s computers can perform billions of operations within a
second, and with the developments in parallel processing, analyses
of larger and larger electrical systems in a short time frame are
very feasible

9. THE WHEATSTONE BRIDGE
The next application is a simple circuit for the precise measurement of
resistors known as the Wheatstone Bridge. The circuit, invented by
Samuel Hunter Christie (1784-1865) in 1833, was named after Sir Charles
Wheatstone (1802-1875) who ‘found’ and popularized the arrangement in
1843. It consists of an electrical source and a galvanometer that connects
two parallel branches, containing four resistors, three of which are known.
One parallel branch consists of a known and unknown resistor (R4), while
the other branch contains two known resistors.

10. • Kirchoff ’s Current Law yields:
I0 - I1 - I2 = 0
I1 - I5 - I3 = 0
I2 + I5 - I4 = 0
I3 + I4 - I0 = 0
• And Kirchoff ’s Voltage Law yields:
I2R2 - I5R5 - I1R1 = 0
I5R5 + I4R4 - I3R3= 0
I2R2 + I4R4 - E = 0
I1R1 + I3R3 - E = 0

11. In this case, we observe a circuit
that has a 5-volt power supply with
different loops, and its resistors.
Notice now that we have three loops
drawn, all rotating clockwise. Next,
we must drawn loops in which the
current in the circuit travels, called
I1, I2, and I3. I1, I2, and I3 are all
current loops (measured in Amps).

12. We start with the general equation,
𝑛=1
𝑛
𝐼𝑛 ∗ 𝑅𝑛 = 𝑉
Where V is the voltage, I is the current around a loop, and Rn is the total
resistance of the path for the given current In.
Next, we want to look at each loop, and set up an equation, which uses
all paths that touch the loop multiplied by their total resistances where
they touch that path. Observe the following equations:
18I1 – 2I2 -5I3 = 5
-2I1 + 5I2 -3I3 = 0
-3I1 – 5I2 +9I3 = 0
The coefficients for I1, I2, and I3 are all the
total resistances for those loops, which have
unknown current, and they are set equal to
the total potential difference (voltage) around
that loop. We can then put these equations
into an augmented

13. When we put the system is put into an augmented matrix, we get the
following:
18 − 2 − 5 5
−2 5 − 3 0
−5 − 3 9 0
When we row reduce this matrix, we get
1 0 0 0.4215
0 1 0 0.3864
0 0 1 0.3630
From this, we can
determine what the
current through I1, I2, and
I3 are.

14. Thank You