# Elementary Questions about a Matrix

## Problem 693

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, $a_{23}-a_{31}=-3-0=-3$.