```html
<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Dot Grid Transformer</title>
    <style>
        body {
            font-family: Arial, sans-serif;
            display: flex;
            justify-content: center;
            align-items: center;
            height: 100vh;
            margin: 0;
            background-color: #f5f5f5;
        }

        #canvas {
            border: 1px solid #000;
        }

        form {
            display: flex;
            flex-direction: column;
            margin-bottom: 10px;
        }

        input {
            margin-bottom: 5px;
            width: 100%;
        }

        button {
            width: 100%;
        }
    </style>
</head>
<body>
    <div>
        <form id="matrixForm">
            <label for="matrix">Enter a 2x2 transformation matrix (comma-separated):</label>
            <input type="text" id="matrix" placeholder="1,0,0,1" required>
            <button type="submit">Transform</button>
        </form>
        <canvas id="canvas" width="300" height="300"></canvas>
    </div>
    <script>
        const canvas = document.getElementById('canvas');
        const ctx = canvas.getContext('2d');

        let gridSize = 10;
        let dotSize = 2;
        let dots = [];

        function initGrid() {
            for (let x = 0; x <= canvas.width; x += gridSize) {
                for (let y = 0; y <= canvas.height; y += gridSize) {
                    dots.push({x, y});
                }
            }
        }

        function drawGrid() {
            ctx.clearRect(0, 0, canvas.width, canvas.height);
            ctx.fillStyle = '#000';
            dots.forEach(dot => {
                ctx.beginPath();
                ctx.arc(dot.x, dot.y, dotSize, 0, Math.PI * 2);
                ctx.fill();
            });
        }

        function transformDots(matrix) {
            dots = dots.map(dot => {
                const newX = dot.x * matrix[0] + dot.y * matrix[1];
                const newY = dot.x * matrix[2] + dot.y * matrix[3];
                return {x: newX, y: newY};
            });
        }

        function onMatrixFormSubmit(e) {
            e.preventDefault();
            const matrixInput = document.getElementById('matrix');
            const matrixString = matrixInput.value.trim();
            const matrixValues = matrixString.split(',').map(val => parseFloat(val));

            if (matrixValues.length !== 4 || matrixValues.some(isNaN)) {
                alert('Invalid matrix format. Please enter 4 comma-separated numbers.');
                return;
            }

            transformDots(matrixValues);
            drawGrid();
        }

        document.getElementById('matrixForm').addEventListener('submit', onMatrixFormSubmit);

        initGrid();
        drawGrid();
    </script>
</body>
</html>

```

This code creates a simple website with a canvas displaying a grid of dots. The user can input a 2x2 transformation matrix to transform the grid. The HTML structure contains a form for the user to input the matrix values, a canvas to draw the grid, and JavaScript code to handle the grid transformation and rendering.
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