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:

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