To find the size of the matrix and determine its type, we'll analyze the given matrix:
[tex]\[
\left[\begin{array}{lll}
4 & 9 & 5 \\
0 & 5 & 4 \\
9 & 0 & 4
\end{array}\right]
\][/tex]
Step 1: Determine the number of rows and columns.
- Number of rows: Count the horizontal lines of elements. There are 3 rows.
- First row: [tex]\([4, 9, 5]\)[/tex]
- Second row: [tex]\([0, 5, 4]\)[/tex]
- Third row: [tex]\([9, 0, 4]\)[/tex]
- Number of columns: Count the vertical lines of elements. There are also 3 columns.
- First column: [tex]\([4, 0, 9]\)[/tex]
- Second column: [tex]\([9, 5, 0]\)[/tex]
- Third column: [tex]\([5, 4, 4]\)[/tex]
Thus, the matrix is [tex]\(3 \times 3\)[/tex].
Step 2: Determine if the matrix is a square matrix.
A square matrix has the same number of rows and columns.
- Here, the matrix has 3 rows and 3 columns.
- Since the number of rows equals the number of columns (3 = 3), this matrix is a square matrix.
Step 3: Determine if the matrix is a column matrix.
A column matrix has only one column and one or more rows.
- This matrix has 3 columns, so it is not a column matrix.
Step 4: Determine if the matrix is a row matrix.
A row matrix has only one row and one or more columns.
- This matrix has 3 rows, so it is not a row matrix.
Summary:
- The size of the matrix is [tex]\(3 \times 3\)[/tex].
- It is a square matrix.
- It is neither a column matrix nor a row matrix.
So, in conclusion, the matrix is [tex]\(3 \times 3\)[/tex] in size.
