Linear Algebra and Its Applications · Problem 1.4.2

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · matrix-notation-and-multiplication

Problem

Working a column at a time, compute the products

\begin{bmatrix}4 & 1\\5 & 1\\6 & 1\end{bmatrix}\begin{bmatrix}1\\3\end{bmatrix} \quad \text{and} \quad \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{bmatrix}\begin{bmatrix}0\\1\\0\end{bmatrix} \quad \text{and} \quad \begin{bmatrix}4 & 3\\6 & 6\\8 & 9\end{bmatrix}\begin{bmatrix}\frac{1}{2}\\\frac{1}{3}\end{bmatrix}.