Question

In matrix product HF, the value in the fourth row of the first column is

Answer 1

\[\textbf H \textbf F=\left[\begin{array}\ 1&-2&-1&3\\2&0&4&-1\\3&5&-2&2\\1&-1&0&0\end{array}\right] \left[\begin{array}\ 1&0\\5&-3\\-2&6\\-1&5\end{array}\right] \]

Answer 2

\[= \left[\begin{array}\ 1\times1-2\times5-1\times-2+3\times-1, & 1\times0-2\times-3-1\times6+3\times5\\2\times1+0\times5+4\times-2-1\times-1, & 2\times0+0\times-3+4\times6-1\times5\\ 3\times 1+5\times5-2\times-2+2\times-1, & 3\times0+5\times-3-2\times6+2\times5\\1\times1-1\times5+0\times-2+0\times-1,&1\times0-1\times-3+0\times6+0\times5\end{array}\right] \]

Answer 3

\[= \left[\begin{array}\ 1\times1-2\times5-1\times-2+3\times-1, & 1\times0-2\times-3-1\times6+3\times5\\2\times1+0\times5+4\times-2-1\times-1, & 2\times0+0\times-3+4\times6-1\times5\\ 3\times 1+5\times5-2\times-2+2\times-1, & 3\times0+5\times-3-2\times6+2\times5\\ \color{teal}{1\times1-1\times5+0\times-2+0\times-1},&{1\times0-1\times-3+0\times6+0\times5}\end{array}\right] \]