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Unformatted text preview: Introduction to Programming
Lecture # 43 Math Library Complex number Matrix Quadratic equation and their solution …………….… To design a program properly, we must : – Analyze a problem statement, typically Design Recipe expressed as a word problem examples – Express its essence, abstractly and with – Formulate statements and comments in a precise language i.e. code – Evaluate and revise the activities in light – PAY ATTENTION TO DETAIL of checks and tests and Matrix
• Matrix is nothing but a two dimensional array of numbers • Normally, represented in the form of : • Rows • Columns Example
A= 1 5 9 2 6 10 3 7 11 4 8 12 Three Rows Four Columns i & j are two Integers
i representing the Row number j representing the Column number Operations Performed with Matrix
• Addition of two matrices. • Addition of a scalar and a matrix • Subtraction of two matrices • Subtraction of a scalar from a matrix • Multiplication of two matrices • Multiplication of a scalar with a matrix • Division of a scalar with a matrix • Transpose of a matrix Interface Addition of two Matrices Aij+ Bij = Cij Addition of two Matrices
Size of two matrices must be same Number of rows and columns must be identical for the matrices to be addable Example
2 2 0 4 2 0 5 0 10 1 2 6 10 3 7 11 = 5 9  3 7 9 6 4 10 8 7 1 Cij = Aij  Bij Adding a Scalar to the Matrix Ordinary number added to every element of the matrix Subtracting a Scalar from a Matrix Ordinary number subtracted from every element of the matrix Division of Matrix by a Scalar
Divide every element of Matrix by a scalar number Example
Let : X be a Scalar number A be a Matrix C ij = Aij
X Multiplication of a scalar with a Matrix : Example Let : X is a Scalar number A is a Matrix X*A
X * A ij = Cij Multiply two Matrices 1 5 2 6 * 2 1 4 2 = (1)(2)+(2)(1) (5)(2)+(6)(1) (1)(4)+(2)(2) (5)(4)+(6)(2) Rules Regarding Matrix Multiplication
Number of columns of the 1st Matrix = Number of rows of the 2nd Matrix Rules regarding Matrix Multiplication
First matrix has
– M rows – N columns – N rows – P columns – M rows Second matrix has Resultant matrix will have Transpose of a Matrix
Interchange of rows and columns Transpose of a Matrix Example
1 5 9 2 6 10 3 7 11 1 2 3 5 6 7 9 10 11 Transpose of a Non Square Matrix
Size of matrix change after transpose A
3 ( Rows ) * 4 ( Columns ) Before A T 4 ( Rows ) * 3 ( Columns ) After Next Phase of Analysis
• Determine the Constants • Memory Allocation • What is it’s user interface Interface Interface
Constructor : Parameters are Number of rows Number of columns Display function Plus operator : member operator of the class Subtraction operator : member operator of the class Plus operator : friend of the class Subtraction operator : friend of the class Plus Operator A+X X+A Subtraction Operator AX X–A Interface Multiplication Operator : Member of the Class Multiplication Operator : Friend of the Class Division Operator : Member of the Class Transpose Function : Member of the Class Assignment Operator : Member of the Class += , = : Members of the Class Multiplication Operator A*X X*A Assignment Operator A=B ( Member Operator ) Interface
>> Extraction Operator : Friend Operator << Stream Insertion Operator : Friend Operator Copy Constructor Copy Constructor Assignment Operator Memory Allocation Memory Deallocation ...
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This note was uploaded on 01/12/2010 for the course CS CS 201 taught by Professor Dr.naveedmalik during the Spring '09 term at Virtual University of Pakistan.
 Spring '09
 Dr.NaveedMalik

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