Q15. - Algebra 2

Question

State the dimensions of each matrix.

 

$\left[\begin{array}{cc}16& 8\\ 10& 5\\ 0& 0\end{array}\right]$

Step-by-Step Solution

Answer

The dimension of the matrix $\left[\begin{array}{cc}16& 8\\ 10& 5\\ 0& 0\end{array}\right]$ is $\mathbf{3}\mathbf{\times }\mathbf{2}$.

Step 1 - Count the number of rows

The number of rows of the provided matrix is 3, that is, $\left[\begin{array}{cc}16& 8\end{array}\right]$, $\left[\begin{array}{cc}10& 5\end{array}\right]$, and $\left[\begin{array}{cc}0& 0\end{array}\right]$.

Step 2 – Count the number of columns

The number of columns of the provided matrix is 2, that is, $\left[\begin{array}{c}16\\ 10\\ 0\end{array}\right]$, and $\left[\begin{array}{c}8\\ 5\\ 0\end{array}\right]$.

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 $\left[\begin{array}{cc}16& 8\\ 10& 5\\ 0& 0\end{array}\right]$, the dimension is $3\times 2$.