Multiply matrices and vectors

What you'll learn

1. Represent a vector in component form as a column matrix (column vector).
2. Multiply a matrix by a column vector using the row-dot-product rule.
3. Interpret the matrix-vector product $A\mathbf{v}$ as a linear transformation of $\mathbf{v}$.
4. Identify standard $2 \times 2$ transformations: scaling, reflection over an axis, and rotation by 90°.
5. Compute the composition of two transformations as a single matrix product and explain why order matters.

Prerequisites

• Add, subtract, and multiply matrices
• Add and subtract vectors