Q12. - Algebra 2

Question

State the dimensions of each matrix.

 

$\left[\begin{array}{ccc}0& 0& 8\\ 6& 2& 4\\ 1& 3& 6\\ 5& 9& 2\end{array}\right]$

Step-by-Step Solution

Answer

The dimension of the matrix $\left[\begin{array}{ccc}0& 0& 8\\ 6& 2& 4\\ 1& 3& 6\\ 5& 9& 2\end{array}\right]$ is $\mathbf{4}\mathbf{\times }\mathbf{3}$.

Step 1 - Count the number of rows

The number of rows of the provided matrix is 4, that is, $\left[\begin{array}{ccc}0& 0& 8\end{array}\right]$, $\left[\begin{array}{ccc}6& 2& 4\end{array}\right]$, $\left[\begin{array}{ccc}1& 3& 6\end{array}\right]$, and $\left[\begin{array}{ccc}5& 9& 2\end{array}\right]$.

Step 2 – Count the number of columns

The number of columns of the provided matrix is 3, that is, $\left[\begin{array}{c}0\\ 6\\ 1\\ 5\end{array}\right]$, $\left[\begin{array}{c}0\\ 2\\ 3\\ 9\end{array}\right]$, and $\left[\begin{array}{c}8\\ 4\\ 6\\ 2\end{array}\right]$.

Step 3 – State the dimension

The dimension of a matrix is defined as $m\times n$, where $m$ is the number of rows and $n$ is the number of columns.

Therefore, for the matrix $\left[\begin{array}{ccc}0& 0& 8\\ 6& 2& 4\\ 1& 3& 6\\ 5& 9& 2\end{array}\right]$, the dimension is $4\times 3$.