Linear Algebra and Its Applications · Problem 1.4.11

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · matrix-notation-and-multiplication

Problem

The first row of

AB

is a linear combination of all the rows of

B

. What are the coefficients in this combination, and what is the first row of

AB

, if

A = \begin{bmatrix}2 & 1 & 4\\0 & -1 & 1\end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix}1 & 1\\0 & 1\\1 & 0\end{bmatrix}?