Let
\[A=\begin{bmatrix}
-5 & 0 & 1 & 2 \\
3 &8 & -3 & 7 \\
0 & 11 & 13 & 28
\end{bmatrix}.\]

(a) What is the size of the matrix $A$?
(b) What is the third column of $A$?
(c) Let $a_{ij}$ be the $(i,j)$-entry of $A$. Calculate $a_{23}-a_{31}$.

Solution.

(a) What is the size of the matrix $A$?

The matrix $A$ has three rows and four columns. Thus, the size of $A$ is $3$ by $4$, or $3\times 4$.

(b) What is the third column of $A$?

The third column of $A$ is $\begin{bmatrix}
1 \\
-3 \\
13
\end{bmatrix}$.

Calculate $a_{23}-a_{31}$.

We see that $a_{23}=-3$ and $a_{31}=0$. Thus, $a_{23}-a_{31}=-3-0=-3$.

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