linear algebra and vector
TRANSCRIPT
By: AnwAr AliLinear Algebra
﷽
Outline
What is Linear Algebra?
What are Vectors?
6 / 1 6 / 2 0 1 6
1
Linear algebra is the study of vectors and linear
transformations.
In broad terms, vectors are things you can add
and linear functions are very
special functions of vectors that respect vector
addition. To understand this
a little better, lets try some examples.
WHAT IS LINEAR ALGEBRA?
6 / 1 6 / 2 0 1 6
2
Here are some examples of things that can be added:
Example 1 (Vector Addition)
(A) Numbers: If x and y are numbers then so is x + y.
WHAT ARE VECTORS?
6 / 1 6 / 2 0 1 6
3
WHAT ARE VECTORS?
6 / 1 6 / 2 0 1 6
4
Numbers are not the only things that are vectors, as
examples C,D,
and E show. Because they \can be added", you should
now start thinking of all the above objects as vectors!
In the above examples, however, notice that the vector
addition rule stems from the rules for adding numbers.
WHAT ARE VECTORS?
6 / 1 6 / 2 0 1 6
5
When adding the same vector over and over, for
example
x + x ; x + x + x ; x + x + x + x ; : : : ;
we will write
2x ; 3x ; 4x ; : : : ;
WHAT ARE VECTORS?
6 / 1 6 / 2 0 1 6
6
WHAT ARE VECTORS?
6 / 1 6 / 2 0 1 6
7
Now the conclusion is that;
Vectors are things you can add and scalar
multiply.
WHAT ARE VECTORS?
Thank You
6 / 1 6 / 2 0 1 6
8
﷽
6 / 1 6 / 2 0 1 6
9
TOPIC
MATRICES
By: Ghulam Raza
6 / 1 6 / 2 0 1 6
10
Matrices: are linear functions of a certain kind. One
way to learn about them
is by studying systems of linear equations.
Example 4 A room contains x bags and y boxes of
fruit:
WHAT ARE MATRICES?
6 / 1 6 / 2 0 1 6
11
WHAT ARE MATRICES?
6 / 1 6 / 2 0 1 6
12
Each bag contains 2 apples and 4 bananas and each box
contains 6 apples and 8 bananas.
There are 20 apples and 28 bananas in the room. Find x and
y.
The values are the numbers x and y that simultaneously
make both of the following
equations true:
2 x + 6 y = 20
4 x + 8 y = 28 :
WHAT ARE MATRICES?
6 / 1 6 / 2 0 1 6
13
WHAT ARE MATRICES?
6 / 1 6 / 2 0 1 6
14
Thank You
6 / 1 6 / 2 0 1 6
15