In this project, we are interested in how certain fractals can be generated by using introductory linear algebra techniques. A fractal is an object or a structure that is self-similar in all length scales. Sierpinski Carpet and Sierpinski Triangle are two classic examples of fractals. Fractals have many applications in real life, for instance, in imaging, art and biological sciences. In this project, we apply classes of linear transformation to describe and generate fractals in the Euclidean plane, and we generate different examples of fractal using MATLAB.