Practical - 4 IWD

 AIM : Write a script to perform 3x3 matrix Multiplication.

3×3 Matrix Multiplication using PHP

📌 Theory (For Exam)

  • Matrix multiplication is possible only if
    Number of columns of Matrix A = Number of rows of Matrix B

  • For 3×3 matrices, the result is also a 3×3 matrix

  • Formula used:

C[i][j]=∑k=02A[i][k]×B[k][j]C[i][j] = \sum_{k=0}^{2} A[i][k] \times B[k][j]

✅ PHP Script for 3×3 Matrix Multiplication

<?php
// Define first 3x3 matrix
$A = array(
    array(1, 2, 3),
    array(4, 5, 6),
    array(7, 8, 9)
);

// Define second 3x3 matrix
$B = array(
    array(9, 8, 7),
    array(6, 5, 4),
    array(3, 2, 1)
);

// Initialize result matrix with zeros
$result = array(
    array(0, 0, 0),
    array(0, 0, 0),
    array(0, 0, 0)
);

// Matrix multiplication logic
for ($i = 0; $i < 3; $i++) {
    for ($j = 0; $j < 3; $j++) {
        for ($k = 0; $k < 3; $k++) {
            $result[$i][$j] += $A[$i][$k] * $B[$k][$j];
        }
    }
}
?>

<!DOCTYPE html>
<html>
<head>
    <title>3x3 Matrix Multiplication</title>
    <style>
        table {
            border-collapse: collapse;
            margin: 10px;
        }
        td {
            border: 1px solid black;
            padding: 8px;
            text-align: center;
        }
    </style>
</head>
<body>

<h2>Matrix A</h2>
<table>
<?php
for ($i = 0; $i < 3; $i++) {
    echo "<tr>";
    for ($j = 0; $j < 3; $j++) {
        echo "<td>{$A[$i][$j]}</td>";
    }
    echo "</tr>";
}
?>
</table>

<h2>Matrix B</h2>
<table>
<?php
for ($i = 0; $i < 3; $i++) {
    echo "<tr>";
    for ($j = 0; $j < 3; $j++) {
        echo "<td>{$B[$i][$j]}</td>";
    }
    echo "</tr>";
}
?>
</table>

<h2>Resultant Matrix (A × B)</h2>
<table>
<?php
for ($i = 0; $i < 3; $i++) {
    echo "<tr>";
    for ($j = 0; $j < 3; $j++) {
        echo "<td>{$result[$i][$j]}</td>";
    }
    echo "</tr>";
}
?>
</table>

</body>
</html>

🧠 Step-by-Step Explanation

1️⃣ Matrix Declaration

$A = array(...);
$B = array(...);

  • Two 3×3 matrices are defined using 2D arrays

2️⃣ Result Matrix Initialization

$result = array(
    array(0,0,0),
    array(0,0,0),
    array(0,0,0)
);

  • Stores the final multiplication result

3️⃣ Matrix Multiplication Logic

for ($i = 0; $i < 3; $i++)
    for ($j = 0; $j < 3; $j++)
        for ($k = 0; $k < 3; $k++)
            $result[$i][$j] += $A[$i][$k] * $B[$k][$j];

  • Outer loop ($i) → Row of Matrix A

  • Middle loop ($j) → Column of Matrix B

  • Inner loop ($k) → Performs multiplication and addition

📊 Sample Output

Matrix A        Matrix B        Result (A × B)
1  2  3         9  8  7         30  24  18
4  5  6         6  5  4         84  69  54
7  8  9         3  2  1         138 114 90

🎓 Viva / Exam Questions

Q1. Why three loops are used?
👉 To traverse rows, columns, and perform multiplication.

Q2. Condition for matrix multiplication?
👉 Columns of first matrix = Rows of second matrix.

Q3. Data structure used?
👉 Two-dimensional array.

Q4. Size of resultant matrix?
👉 Same as rows of first matrix × columns of second matrix.

Comments

Post a Comment

Popular posts from this blog

Unit I - Introduction to PHP

  1. Introduction to PHP 1.1 Introduction to Static and Dynamic Websites Static Website Content is fixed and does not change automatically. Created using HTML and CSS . Same content is shown to all users. Example: A college notice page written only in HTML. < h1 >Welcome to Our College </ h1 > < p >Admission Open </ p > Dynamic Website Content changes based on user interaction or database. Uses server-side languages like PHP . Can display different data to different users. Example: Login system, online result system, feedback form. 1.2 Introduction to PHP and Its History PHP stands for Hypertext Preprocessor . It is a server-side scripting language . PHP code runs on the server and sends output to the browser as HTML. History of PHP Created by Rasmus Lerdorf in 1994 . Initially called Personal Home Page . Later developed into a powerful web development language. Widely used with MySQL for database-d...
Read more

Practical - 1 IWD

  Aim To install and configure PHP, Web Server, and MySQL database using XAMPP / WAMP / LAMP / MAMP and create a web page to display “Hello World” . Software Required XAMPP / WAMP / LAMP / MAMP Web Browser (Chrome / Firefox) Text Editor (Notepad / VS Code) Theory PHP is a server-side scripting language. Apache is a web server. MySQL is a relational database. XAMPP / WAMP / LAMP / MAMP are software packages that provide: Web Server (Apache) PHP MySQL phpMyAdmin Installation and Configuration Steps Using XAMPP (Windows / Linux / macOS) Step 1: Download XAMPP Download XAMPP installer from official website. Run the installer and select: Apache MySQL PHP phpMyAdmin Step 2: Install XAMPP Follow installation wizard. Default installation path: C:\xampp\ Step 3: Start Services Open XAMPP Control Panel Start: Apache MySQL ✔ Green indicator confirms successful start. Step 4: Verify Ins...
Read more

Practical - 10 IWD

  Aim : Employee Management System using PHP & MySQL Database Creation CREATE DATABASE employee_db; USE employee_db; CREATE TABLE employees ( emp_id INT AUTO_INCREMENT PRIMARY KEY , name VARCHAR ( 100 ), email VARCHAR ( 100 ), password VARCHAR ( 100 ), department VARCHAR ( 50 ), salary FLOAT ); Database Connection (db.php) <?php $conn = mysqli_connect ( "localhost" , "root" , "" , "employee_db" ); if (! $conn ) { die ( "Database Connection Failed" ); } ?> i) Employee Registration Form (register.php) < form method = "post" > Name: < input type = "text" name = "name" > < br > Email: < input type = "email" name = "email" > < br > Password: < input type = "password" name = "password" > < br > Department: < input type = "text" name = "department...
Read more