Q14. - Algebra 2

Question

State the dimensions of each matrix.

 

14. $\left[\begin{array}{ccccc}17& -2& 8& -9& 6\\ 5& 11& 20& -1& 4\end{array}\right]$

Step-by-Step Solution

Answer

The dimension of the matrix $\left[\begin{array}{ccccc}17& -2& 8& -9& 6\\ 5& 11& 20& -1& 4\end{array}\right]$ is $\mathbf{2}\mathbf{\times }\mathbf{5}$.

Step 1 - Count the number of rows

The number of rows of the provided matrix is 2, that is, $\left[\begin{array}{ccccc}17& -2& 8& -9& 6\end{array}\right]$, and $\left[\begin{array}{ccccc}5& 11& 20& -1& 4\end{array}\right]$.

Step 2 – Count the number of columns

The number of columns of the provided matrix is 5, that is, $\left[\begin{array}{c}17\\ 5\end{array}\right]$, $\left[\begin{array}{c}-2\\ 11\end{array}\right]$, $\left[\begin{array}{c}8\\ 20\end{array}\right]$, $\left[\begin{array}{c}-9\\ -1\end{array}\right]$, and $\left[\begin{array}{c}6\\ 4\end{array}\right]$.

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 $\left[\begin{array}{ccccc}17& -2& 8& -9& 6\\ 5& 11& 20& -1& 4\end{array}\right]$, the dimension is $2\times 5$.