To determine the order of the given matrix, we need to identify the number of rows and the number of columns it has.
Consider the matrix:
[tex]\[
\left[\begin{array}{ccc}
-1 & 0 & 2 \\
4 & 5 & 8
\end{array}\right]
\][/tex]
### Step-by-Step Solution:
1. Count the number of rows:
The matrix has elements arranged in horizontal lines, which are called rows. Here, we can observe that there are two horizontal lines of elements.
[tex]\[
\begin{array}{c}
\text{Row 1: } [-1, 0, 2] \\
\text{Row 2: } [4, 5, 8] \\
\end{array}
\][/tex]
So, the matrix has 2 rows.
2. Count the number of columns:
The elements are also arranged in vertical lines, called columns. By looking at the matrix, we can see that each row contains three elements.
[tex]\[
\begin{array}{ccc}
\text{Column 1} & \text{Column 2} & \text{Column 3} \\
-1 & 0 & 2 \\
4 & 5 & 8 \\
\end{array}
\][/tex]
Thus, the matrix has 3 columns.
3. Determine the order of the matrix:
The order of a matrix is given by the number of rows followed by the number of columns. Based on our counts:
- Number of rows = 2
- Number of columns = 3
Therefore, the order of the matrix [tex]\(\left[\begin{array}{ccc}-1 & 0 & 2 \\ 4 & 5 & 8\end{array}\right]\)[/tex] is [tex]\(2 \times 3\)[/tex].
