Diagonal Matrix Exercise (with Solution)

Exercise:

\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix} & \textbf{Diagonal Matrix?} \\
\hline
\begin{pmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 4 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 9 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & ? \\
\hline
\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} & ? \\
\hline
\end{array}
\]

Solution:

\[
\begin{array}{|c|c|}
\hline
\textbf{Matrix} & \textbf{Diagonal Matrix?} \\
\hline
\begin{pmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} & \text{No} \\
\hline
\begin{pmatrix} 4 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 9 \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & \text{Yes} \\
\hline
\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} & \text{No} \\
\hline
\end{array}
\]