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Q12.

Expert-verified
Found in: Page 156

Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

State the dimensions of each matrix.$\left[\begin{array}{ccc}0& 0& 8\\ 6& 2& 4\\ 1& 3& 6\\ 5& 9& 2\end{array}\right]$

The dimension of the matrix $\left[\begin{array}{ccc}0& 0& 8\\ 6& 2& 4\\ 1& 3& 6\\ 5& 9& 2\end{array}\right]$ is $\mathbf{4}\mathbf{×}\mathbf{3}$.

See the step by step solution

Step 1 - Count the number of rows

The number of rows of the provided matrix is 4, that is, $\left[\begin{array}{ccc}0& 0& 8\end{array}\right]$, $\left[\begin{array}{ccc}6& 2& 4\end{array}\right]$, $\left[\begin{array}{ccc}1& 3& 6\end{array}\right]$, and $\left[\begin{array}{ccc}5& 9& 2\end{array}\right]$.

Step 2 – Count the number of columns

The number of columns of the provided matrix is 3, that is, $\left[\begin{array}{c}0\\ 6\\ 1\\ 5\end{array}\right]$, $\left[\begin{array}{c}0\\ 2\\ 3\\ 9\end{array}\right]$, and $\left[\begin{array}{c}8\\ 4\\ 6\\ 2\end{array}\right]$.

Step 3 – State the dimension

The dimension of a matrix is defined as $m×n$, where $m$ is the number of rows and localid="1648720004630" $n$ is the number of columns.

Therefore, for the matrix localid="1648719994942" $\left[\begin{array}{ccc}0& 0& 8\\ 6& 2& 4\\ 1& 3& 6\\ 5& 9& 2\end{array}\right]$, the dimension is localid="1648719999288" $4×3$.