Problem
a. Give the order of the given matrix. b. If $A=\left[a_{i j}\right]$, identify $a_{32}$ and $a_{23}$, if possible. $\left[\begin{array}{rrr}2 & -6 & 4 \\ -2 & 3 & -8\end{array}\right]$ a. The order of the given matrix, in the form $m \times n$, is $2 \times 3$. b. Identify $a_{32}$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $a_{32}=$ B. Element $\mathrm{a}_{32}$ does not exist. Identify $a_{23}$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $a_{23}=$ B. Element $\mathrm{a}_{23}$ does not exist.
Solution
Step 1 ：The order of a matrix is given by the number of rows and columns it has. In this case, the matrix has 2 rows and 3 columns, so its order is \(2 \times 3\).
Step 2 ：The element \(a_{32}\) refers to the element in the 3rd row and 2nd column. However, this matrix only has 2 rows, so \(a_{32}\) does not exist.
Step 3 ：The element \(a_{23}\) refers to the element in the 2nd row and 3rd column. This element does exist in the matrix and is \(-8\).
Step 4 ：Final Answer: The order of the matrix is \(\boxed{2 \times 3}\). Element \(a_{32}\) does not exist. Element \(a_{23}\) is \(\boxed{-8}\).
