Q13. - Algebra 2

Question

State the dimensions of each matrix.

 

13. $\left[\begin{array}{ccc}-3& 17& -22\\ 9& 31& 16\\ 20& -15& 4\end{array}\right]$

Step-by-Step Solution

Answer

The dimension of the matrix $\left[\begin{array}{ccc}-3& 17& -22\\ 9& 31& 16\\ 20& -15& 4\end{array}\right]$ is $\mathbf{3}\mathbf{\times }\mathbf{3}$.

Step 1 - Count the number of rows

The number of rows of the provided matrix is 3, that is, $\left[\begin{array}{ccc}-3& 17& -22\end{array}\right]$, $\left[\begin{array}{ccc}9& 31& 16\end{array}\right]$, and $\left[\begin{array}{ccc}20& -15& 4\end{array}\right]$.

Step 2 – Count the number of columns

The number of columns of the provided matrix is 3, that is, $\left[\begin{array}{c}-3\\ 9\\ 20\end{array}\right]$, $\left[\begin{array}{c}17\\ 31\\ -15\end{array}\right]$, and $\left[\begin{array}{c}-22\\ 16\\ 4\end{array}\right]$.

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 $\left[\begin{array}{ccc}-3& 17& -22\\ 9& 31& 16\\ 20& -15& 4\end{array}\right]$, the dimension is .