Q5. - Algebra 2

Question

State the dimensions of each matrix.

 

5. $\left[\begin{array}{cccc}10& -6& 18& 0\\ -7& 5& 2& 4\\ 3& 11& 9& 7\\ & & & \end{array}\right]$

Step-by-Step Solution

Answer

The dimension of the matrix $\left[\begin{array}{cccc}10& -6& 18& 0\\ -7& 5& 2& 4\\ 3& 11& 9& 7\\ & & & \end{array}\right]$ is $\mathbf{3}\mathbf{\times }\mathbf{4}$.

Step 1 - Count the number of rows

The number of rows of the provided matrix is 3, that is, $\left[\begin{array}{cccc}10& -6& 18& 0\\ & & & \end{array}\right]$, $\left[\begin{array}{cccc}-7& 5& 2& 4\\ & & & \end{array}\right]$, and $\left[\begin{array}{cccc}3& 11& 9& 7\\ & & & \end{array}\right]$.

Step 2 – Count the number of columns

The number of columns of the provided matrix is 4, that is, $\left[\begin{array}{c}10\\ -7\\ 3\\ \end{array}\right]$, $\left[\begin{array}{c}-6\\ 5\\ 11\\ \end{array}\right]$, $\left[\begin{array}{c}18\\ 2\\ 9\\ \end{array}\right]$, and $\left[\begin{array}{c}0\\ 4\\ 7\\ \end{array}\right]$.

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 $\left[\begin{array}{cccc}10& -6& 18& 0\\ -7& 5& 2& 4\\ 3& 11& 9& 7\\ & & & \end{array}\right]$, the dimension is $3\times 4$.