# Arrays 

**Q1. Write a program in 'C' language that accepts two matrices as input and prints their product**

**Input: Two matrices A and B in two-dimensional arrays**

**Output: Matrix C' which is result of AXB in the form of two dimensional array**

ANS-1.

### 1\. Header File

```c
#include <stdio.h>
```

**stdio.h** ek standard C library hai.

Isme **printf()** aur **scanf()** jaise functions available hote hain.

**printf()** → output print karne ke liye

**scanf()** → input lene ke liye

### 2\. Main Function

```c
int main() {
```

Program ki execution **main()** se start hoti hai.

### **3\. Matrices Declare** Karna

```c
int A[10][10], B[10][10], C[10][10] = {0};
```

Yahan 3 two-dimensional arrays banaye:

A → First matrix

B → Second matrix

C → Result matrix

```c
A = First Matrix
B = Second Matrix
C = A × B
```

\[10\]\[10\] ka matlab maximum 10 rows × 10 columns.

**{0} kyun?**

```c
C[10][10] = {0};
```

Result matrix ke saare elements initially 0 honge.

Ye important hai kyunki baad mein hum likhenge:

```c
C[i][j] += A[i][k] * B[k][j];
```

### **4\. Variables**

```c
int r1, c1, r2, c2, i, j, k;
```

In variables ka meaning:

| Variable | Meaning |
| --- | --- |
| `r1` | Matrix A ki rows |
| `c1` | Matrix A ke columns |
| `r2` | Matrix B ki rows |
| `c2` | Matrix B ke columns |
| `i` | Row ke liye |
| `j` | Column ke liye |
| `k` | Multiplication ke liye |

### 5\. Matrix A ka Size Lena

```c
printf("Enter rows and columns of A: ");
scanf("%d %d", &r1, &c1);User se Matrix A ki:
```

User se Matrix A ki:

*   rows
    
*   columns
    

li ja rahi hain.

Example:

```c
2 2
```

Matlab A hai:

```c
2 × 2
```

### **6\. Matrix B ka Size Lena**

```c
printf("Enter rows and columns of B: "); 
scanf("%d %d", &r2, &c2);
```

Similarly Matrix B ka size input hota hai.

Example:

```c
2 2 
```

Matlab B bhi:

```c
2 × 2
```

7\. Multiplication Possible Hai Ya Nahi?

```c
if (c1 != r2)
{
    printf("Matrix multiplication not possible");
    return 0;
}
```

Ye sabse important condition hai.

Matrix multiplication ke liye:

```c
A ke columns = B ki rows
```

Example:

```c
A = 2 × 3
B = 3 × 2
```

Multiplication possible hai because:

```c
3 = 3
```

Lekin:

```c
A = 2 × 3 
B = 2 × 2
```

Possible nahi hai because:

```c
3 ≠ 2
```

### **8\. Matrix A Input**

```c
printf("Enter matrix A:\n");

for(i = 0; i < r1; i++)
    for(j = 0; j < c1; j++)
        scanf("%d", &A[i][j]);
```

Yahan nested loop use hua hai.

Outer loop

```c
for(i = 0; i < r1; i++)
```

Rows ko control karta hai.

Inner loop

```c
for(j = 0; j < c1; j++)
```

Columns ko control karta hai.

```c
scanf("%d", &A[i][j]);
```

Input Har position par value store hoti hai.

For example:

```c
1 2 
3 4
```

Array mein:

```c
A[0][0] = 1
A[0][1] = 2
A[1][0] = 3
A[1][1] = 4
```

### **9\. Matrix B Input**

```c
printf("Enter matrix B:\n");

for(i = 0; i < r2; i++)
 for(j = 0; j < c2; j++)
 scanf("%d", &B[i][j]);
```

Exactly same process Matrix B ke liye.

Example:

```c
5 6 7 8 
```

⭐ 10. Main Matrix Multiplication

Ye program ka sabse important part hai:

```c
for(i = 0; i < r1; i++)
    for(j = 0; j < c2; j++)
        for(k = 0; k < c1; k++)
            C[i][j] += A[i][k] * B[k][j];
```

Yahan 3 loops hain.

`i` → Row

```c
for(i = 0; i < r1; i++)
```

Result matrix ki row select karta hai.

`j` → Column

```c
 for(j = 0; j < c2; j++)
```

Result matrix ka column select karta hai.

`k` → Multiplication

```c
for(k = 0; k < c1; k++)
```

A aur B ke corresponding elements ko multiply karta hai.

Example se samjho 🔥

Suppose:

```c
A = 1 2 3 4
```

and

```c
B = 5 6 7 8
```

Toh:

```c
C[0][0] C[0][0] =    A[0][0] × B[0][0] 
                    +A[0][1] × B[1][0]
    = 1×5 + 2×7

    = 5 + 14

    = 19
```

C\[0\]\[1\]

```c
= 1×6 + 2×8
= 6 + 16
= 22
```

C\[1\]\[0\]

```c
= 3×5 + 4×7
= 15 + 28
= 43
```

C\[1\]\[1\]

```c
= 3×6 + 4×8
= 18 + 32
= 50
```

So final result:

```c
19 22
43 50
```

### **11\. Result Print Karna**

```c
printf("Product Matrix C:\n");

for(i = 0; i < r1; i++)
{
    for(j = 0; j < c2; j++)
        printf("%d ", C[i][j]);

    printf("\n");
}
```

Ye result matrix ko row-by-row print karta hai.

Output:

Product Matrix C:

```c
Product Matrix C:
19 22
43 50
```

### **12\. Program End**

```c
return 0;
```

Iska matlab program successfully end ho gaya.

🧠 Exam ke liye yaad rakhne wali 3 cheezein

1️⃣ Matrix declaration

```c
int A[10][10], B[10][10], C[10][10] = {0};
```

2️⃣ Multiplication condition

```c
Columns of A = Rows of B
```

3️⃣ Main formula

```c
C[i][j] += A[i][k] * B[k][j];
```

Simple trick: i = Row, j = Column, k = Multiply & Add.

## **<mark class="bg-yellow-200 dark:bg-yellow-500/30">Let see the Overall Code</mark>**

```c
#include <stdio.h>

int main()
{
    int A[10][10], B[10][10], C[10][10] = {0};
    int r1, c1, r2, c2, i, j, k;

    printf("Enter rows and columns of A: ");
    scanf("%d %d", &r1, &c1);

    printf("Enter rows and columns of B: ");
    scanf("%d %d", &r2, &c2);

    if (c1 != r2)
    {
        printf("Matrix multiplication not possible");
        return 0;
    }

    printf("Enter matrix A:\n");
    for(i = 0; i < r1; i++)
        for(j = 0; j < c1; j++)
            scanf("%d", &A[i][j]);

    printf("Enter matrix B:\n");
    for(i = 0; i < r2; i++)
        for(j = 0; j < c2; j++)
            scanf("%d", &B[i][j]);

    for(i = 0; i < r1; i++)
        for(j = 0; j < c2; j++)
            for(k = 0; k < c1; k++)
                C[i][j] += A[i][k] * B[k][j];

    printf("Product Matrix C:\n");
    for(i = 0; i < r1; i++)
    {
        for(j = 0; j < c2; j++)
            printf("%d ", C[i][j]);
        printf("\n");
    }

    return 0;
}
```

### Example

**Input:**

```c
Enter rows and columns of A: 2 2
Enter rows and columns of B: 2 2

Enter matrix A:
1 2
3 4

Enter matrix B:
5 6
7 8
```

Output:

```c
Product Matrix C:
19 22
43 50
```

Main Formulla:

```c
C[i][j] = C[i][j] + A[i][k] × B[k][j]
```

**Condition:** `c1 == r2` must be true for `A × B` multiplication.

If u have to run the Code:

https://www.onlinegdb.com/online\_c\_compiler