This document discusses two-dimensional arrays or matrices in C/C++. It explains that a 2D array requires two sets of square brackets in the declaration and reserves a block of contiguous memory. Elements can be initialized row-wise or individually and access follows the pattern of array[row][column]. Operations like addition and multiplication on matrices are demonstrated using 2D arrays where each element is the sum or product of corresponding elements of the arrays being operated on.

1. 2D-Array
Prepared By: Mr. Sangram A. Patil
Assistant Professor PVPIT,Budhgaon

2. Two Dimensional Array
 2D Array is called as Matrix
 Requires pair of square brackets.
 Declaration Syntax
Datatype Array_name[size][size];
Example:
int m[2][3];
float m2[4][4];
 m is 2D array of integer type having subscript each of capacity.
 m is array of having two rows and three columns.

3. Two Dimensional Array
 D array m declared as two arrays with each have three columns.
[0][0] [0][1] [0][2]
[1][0] [1][1] [1][2]
Col 0 Col 1 Col 2
Row 0
Row 1

4.  Array reserves certain amount of memory.
m[0][0] m[0][1] m[0][2] m[1][0] m[1][1] M[1][2]
m

5. Initialization of 2D array
 Assigning initial values to multidimensional array.
 Rules:
1. Last subscript (right most) increase most rapidly.
2. First subscript (left most) increase least rapidly.
 Elements are assigned to 2d array row wise.
 Example:
int m[2][3]={10,20,30,40,50,60};
or
int m[2][3]={{10,20,30},{40,50,60}};
10 20 30
40 50 60
0 1 2
0
1

6.  Memory map
10 20 30 40 50 60
[0][0] [0][1] [0][2] [1][0] [1][1] [1][2]
m

7. Matrix addition
10 20 30
40 50 60
70 80 90
5 6 7
8 9 10
11 12 13
15 26 37
48 59 70
81 92 103
0
1
2
0 1 2
A B C
+ =
C[0][0]=A[0][0]+B[0][0]
C[0][1]=A[0][1]+B[0][1]
C[0][2]=A[0][2]+B[0][2]
C[1][0]=A[1][0]+B[1][0]
C[1][1]=A[1][1]+B[1][1]
C[1][2]=A[1][2]+B[1][2]
C[2][0]=A[2][0]+B[2][0]
C[2][1]=A[2][1]+B[2][1]
C[2][2]=A[2][2]+B[2][2]

8. Matrix Multiplication
10 20 10
4 5 6
2 3 5
3 2 4
3 3 9
4 4 2
130 120 240
51 47 73
35 33 45
x =
C[0][0]=A[0][0]*B[0][0]+A[0][1]*B[1][0]+A[0][2]*B[2][0]
C[0][1]=A[0][0]*B[0][1]+A[0][1]*B[1][1]+A[0][2]*B[2][1]
C[0][2]=A[0][0]*B[0][2]+A[0][1]*B[1][2]+A[0][2]*B[2][2]
C[1][0]=A[1][0]*B[0][0]+A[1][1]*B[1][0]+A[1][2]*B[2][0]
C[1][1]=A[1][0]*B[0][1]+A[1][1]*B[1][1]+A[1][2]*B[2][1]
C[1][1]=A[1][0]*B[0][2]+A[1][1]*B[1][2]+A[1][2]*B[2][2]
C[2][0]=A[2][0]*B[0][0]+A[2][1]*B[1][0]+A[2][2]*B[2][0]
C[2][1]=A[2][0]*B[0][1]+A[2][1]*B[1][1]+A[2][2]*B[2][1]
C[2][0]=A[2][0]*B[0][2]+A[2][0]*B[1][2]+A[2][2]*B[2][2]