Linear Algebra and Its Applications · Problem 1.4.1

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · matrix-notation-and-multiplication

Problem

Compute the products

\begin{bmatrix}4 & 0 & 1\\0 & 1 & 0\\4 & 0 & 1\end{bmatrix}\begin{bmatrix}3\\4\\5\end{bmatrix} \quad \text{and} \quad \begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}\begin{bmatrix}5\\-2\\3\end{bmatrix} \quad \text{and} \quad \begin{bmatrix}2 & 0\\1 & 3\end{bmatrix}\begin{bmatrix}1\\1\end{bmatrix}.

For the third one, draw the column vectors

(2,1)

and

(0,3)

. Multiplying by

(1,1)

just adds the vectors (do it graphically).