To determine the dimensions of the given matrix, we need to count the number of rows and the number of columns in the matrix. The matrix in question is:
[tex]\[
\left[\begin{array}{cc}
2 & 8 \\
5 & -1 \\
2 & 0
\end{array}\right]
\][/tex]
Let's identify each part:
1. Rows: The horizontal lines of elements.
- The first row is [tex]\([2, 8]\)[/tex]
- The second row is [tex]\([5, -1]\)[/tex]
- The third row is [tex]\([2, 0]\)[/tex]
By counting, we see that there are 3 rows in total.
2. Columns: The vertical lines of elements.
- The first column is [tex]\([2, 5, 2]\)[/tex]
- The second column is [tex]\([8, -1, 0]\)[/tex]
By counting, we see that there are 2 columns in total.
Thus, the matrix has 3 rows and 2 columns.
The dimensions of the matrix are given as [tex]\( \text{number of rows} \times \text{number of columns} \)[/tex].
Therefore, the dimensions of the matrix are [tex]\( 3 \times 2 \)[/tex].
Checking the given options:
a. [tex]\(2 \times 3\)[/tex]
b. [tex]\(3 \times 2\)[/tex]
c. [tex]\(3 \times 3\)[/tex]
d. [tex]\(3 \times 1\)[/tex]
The correct answer is:
b. [tex]\(3 \times 2\)[/tex]
