Linear algebra
Matrices
Determinant
System of linear equations
Matrix
A matrix is any doubly subscripted array of
elements arranged in rows and columns.
a11 , , a1n
a 21 , , a 2 n
Aij
A
am1 , , amn
Matrices are used to organize information into
c
Imaginary & Complex Numbers
Once upon a time
1 no real solution
-In the set of real numbers, negative numbers do
not have square roots.
-Imaginary numbers were invented so that
negative numbers would have square roots and
certain equations would have solu
MTH108 Business Math I
Lecture 9
Chapter 4
Mathematical functions
Review
Functions
Ways to express a function;
In words; a mapping diagram; using a formula;
by an equation.
Domain and range of a function
Methods to find the domain
Multivariate funct
Objectives
Thestudentwillbeableto:
1. To determine if a relation is a function.
2. To find the value of a function.
SOL: A.7aef
Designed by Skip Tyler, Varina High School
Functions
Afunctionisarelationinwhicheach
elementofthedomainispairedwithexactly
onee
Frequency Distributions
Consider the marks obtained by 10 students in a
mathematics test as given below
55, 36, 95, 73, 60, 42, 25, 78, 75, 62
find
Min mark
mx mark
Average, median and mode marks
Presentation of data be quite time consuming,
particularly
Functions
Domain
Range
f
x
y =f(x)
A function is an operation performed on an input (x) to produce
an output (y = f(x) ).
The Domain of f is the set of all allowable inputs (x values)
The Range of f is the set of all outputs (y values)
To be well defined
Quadratic function
Solve the following quadratic equations
x2 + 6 x + 9 = 0
2x2 6x + 12 = 0
x2 +3 x 4 = 0
Identify the vertex
problem
Assuming no air resistance or forces other
than the Earth's gravity, the height above the
ground at time t of a falli
Answers Assignment No. 6
Draw the right angle triangle if given parameter m<A = 30 o, m<B = 60o and m<C = 90o
sides a = 3, b= 4 and c=?
Answer:
Q.1
Here c= 5
Q.2
Define Supplementary and Complimentary triangle with suitable example.
do your self
Q.3
find
Institute of Professional Phycology (IPP), BUKC
Fall-2016 Semester, Mathematics (MAT- 105)
BS (Phycology)-2 A (Morning)
Tuesday, September 22, 2016
Assignment No. 2
Q.1
Define mathematical functions with suitable examples:
Q.2
Discuss the types of followi
Institute of Professional Psychology (IPP), BUKC
Fall-2016 Semester, Mathematics
BS (Psychology)-2B (Morning)
Tuesday, October 18, 2016
Assignment No. 6
Q.1
Draw the right angle triangle if given parameter m<A = 30 o, m<B = 60o and m<C = 90o
sides a = 3,
Institute of Professional Phycology (IPP), BUKC
Fall-2016 Semester, Mathematics (MAT- 105)
BS (Phycology)-2 A (Morning)
Tuesday, September 22, 2016
Assignment No. 2
Q.1
Define mathematical functions with suitable examples:
Do your self
Q.2
Discuss the typ
Institute of Professional Psychology (IPP), BUKC
Fall-2016 Semester, Mathematics (MAT- 105)
BS (Phycology)-2B (Morning)
Friday, October 7, 2016
Assignment No. 5
Q.1
Find the 17th term of an arithmetic sequence, whose 4 th term is 5 and the common
differen
Institute of Professional Phycology (IPP), BUKC
Fall-2016 Semester, Mathematics (MAT- 105)
BS (Phycology)-2B (Morning)
Thursday, September 8, 2016
Assignment No. 1
Q.1
Describe number system and give at least an example of following number
system:
i) Natu
Institute of Professional Phycology (IPP), BUKC
Fall-2016 Semester, Mathematics (MAT- 105)
BS (Phycology)-2A (Morning)
Assignment No. 3
Q.1
Find the unique solution of given system of linear equation by Inverse matrix approach:
a) 4x 3y = -3
5x y = 10
b)
Institute of Professional Phycology (IPP), BUKC
Fall-2016 Semester, Mathematics (MAT- 105)
BS (Phycology)-2B (Morning)
Thursday, September 8, 2016
Solution Assignment No. 1
Q.1
Describe number system and give at least an example of following number
system
Institute of Professional Phycology (IPP), BUKC
Fall-2016 Semester, Mathematics (MAT- 105)
BS (Phycology)-2B (Morning)
Answers Assignment No. 3
Q.1Identify nature of solution set of the following system of linear equations:
a) 4x 3y = -3 unique solution
5