Perkalian Matriks

\(p\begin{pmatrix} 3 & -1  \\ 2 & -5 \end{pmatrix}+q\begin{pmatrix}1 & 0  \\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 7 & 2  \\ -4 & 23 \end{pmatrix}\)

\(\begin{pmatrix} 3p & -p  \\ 2p & -5p \end{pmatrix}+\begin{pmatrix}q & 0  \\ 0 & q \end{pmatrix} = \begin{pmatrix} 7 & 2  \\ -4 & 23 \end{pmatrix}\)

\(\begin{pmatrix} 3p + q & -p  \\ 2p & -5p + q \end{pmatrix} = \begin{pmatrix} 7 & 2  \\ -4 & 23 \end{pmatrix}\)

\begin{equation*}
\begin{split}
3p + q & = 7 \quad {\color {red} \dotso \: (1)} \\\\
-p & = 2 \quad {\color {red} \dotso \: (2)} \\\\
2p & = -4 \quad {\color {red} \dotso \: (3)} \\\\
-5p + q & = 23 \quad {\color {red} \dotso \: (4)}
\end{split}
\end{equation*}

Dari persamaan (2) didapat nilai \(p = −2\).

Dari persamaan (1) didapat:

\begin{equation*}
\begin{split}
3p + q & = 7 \\\\
3 (-2) + q & = 7 \\\\
-6 + q & = 7 \\\\
q & = 13
\end{split}
\end{equation*}