MTH100 Midterm Short Notes

MTH100 MID TERM SHORT NOTES

Composed By: Sarfraz Talib

Matrix

A rectangular array of number arranged into rows and columns is called matrix OR The combination of rows and columns in square or rectangular form is called matrix

Order of Matrix

The number of rows and columns in a matrix specifies its order. If a matrix M has a rows and a columns the M is said to be of order, m-b-n e.g 1 2 3 1 0 2 is order of 2-by-3

Equal matrix

Two numbers are said to be equal if and only They have same order They corresponding entries are equal e.g 7 0 4 3 3 2 3 2 are equal

Row Matrix

A matrix is called a row matrix, if it has only one row e.g M=[5 3]

Column Matrix

A matrix is called column matrix, if it has only one column e.g 1

Rectangular matrix

A matrix is called rectangular. If the number of rows not equal to number of columns e.g 1 2

Square matrix

A matrix is called square matrix, if the number of rows are equal to number of columns e.g 4 0

Null or Zero matrix

A matrix is called a Null or Zero matrix, if each of its entries is Zero (0) e.g 0

Symmetric matrix

A matrix is called symmetric matrix if At=A e.g 1

Skew Symmetric matrix

A square matrix is called skew symmetric At=-A e.g 0

Scalar matrix

A matrix is called scalar matrix if all the diagonal entries are same e.g 3 0

Diagonal matrix

A square matrix is called diagonal matrix if at least any one of the entries of its diagonal is not zero and non diagonal entries must all be zero e.g 1 0 0

Identity matrix

A diagonal matrix is called identity (unit) matrix if all diagonal entries are 1 e.g 1 0 B

Singular matrix

A square matrix is called singular matrix if the determinant of M is equal to zero I.e. [M]=0

Non singular matrix

A square matrix is called non singular matrix, if the determinant M is not equal to zero i.e |M|¹O e.g 6

Transpose of matrix

A matrix obtained by changing the rows into columns or to columns in to rows of a matrix is called Transpose of matrix

Negative of matrix

Let A be a matrix then its negative –A is obtained by changing the signs of all the entries.

Then

CHAPTER# 2 · REAL AND COMPLEX NUMBERS · Set of real number:

Union of two disjoint sets, the set of rational number Q and the set of irrational number Q`. R= QUQ`

Complex Number:

A number of the form Z=a+bί where a and b are the real numbers and ί= is called complex number. e.g. Z=6+2ί