Q10. - Algebra 2

Question

State the dimensions of each matrix.

 

10. $\left[\begin{array}{ccc}6& -1& 5\\ -2& 3& -4\end{array}\right]$

Step-by-Step Solution

Answer

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

Step 1 - Count the number of rows

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

Step 2 – Count the number of columns

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

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 $\left[\begin{array}{ccc}6& -1& 5\\ -2& 3& -4\\ & & \end{array}\right]$, the dimension is $2\times 3$.