Elementary Linear Algebra - Lecture 0 - Matrix Basics

Matrix transformations change the position, orientation, or size of vectors in space using multiplication. The matrix (0, 1.5, 1.5, 0) swaps the x and y components of any vector and scales them by 1.5. This means if you input a vector like (1, 2), the output would be (3, 1.5). Geometrically, this matrix reflects points across the line y = x and stretches them. It doesn’t preserve angles or lengths, but it keeps the origin fixed and turns lines into other lines, which is a key property of linear