Question

select the correct answer.
what is the order of this matrix?
\

$$\begin{bmatrix}2 & -1 & 0\\\\4 & 1 & -2\\\\3 & -5 & 1\\\\3 & 6 & 1\\\\3 & 1 & 0\\end{bmatrix}$$

\bigcirc a. \\ 2 \times 3
\bigcirc b. \\ 3 \times 5
\bigcirc c. \\ 5 \times 3
\bigcirc d. \\ 3 \times 2

Explanation:

Step1: Recall matrix order definition

The order of a matrix is given by \( \text{number of rows} \times \text{number of columns} \).

Step2: Count rows

Count the number of horizontal rows in the matrix. The matrix has 5 rows (each set of numbers between the brackets: \( [2, -1, 0] \), \( [4, 1, -2] \), \( [3, -5, 1] \), \( [3, 6, 1] \), \( [3, 1, 0] \)).

Step3: Count columns

Count the number of vertical columns. Each row has 3 elements, so there are 3 columns.

Step4: Determine order

Using the order formula (rows × columns), we get \( 5 \times 3 \).

Answer:

C. \( 5 \times 3 \)