Q44. - Algebra 2

Question

State the dimensions of each matrix.

 

44. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Step-by-Step Solution

Answer

The dimension of the matrix is $2\times 2$.

Step 1 - Define the dimension of the matrix

A matrix A with m rows and n columns is a matrix of dimensions $m\times n$.

Step 2 - State an example

Let us consider a matrix $A=\left[\begin{array}{ccc}1& 2& -3\\ 0& 1& 4\end{array}\right]$. Clearly, matrix A has 2 rows and 3 columns, therefore, the dimension of matrix A will be $2\times 3$.

Step 3 - State the dimension of 1 0 0 1

In order to state the dimension of the matrix $\left[\begin{array}{cc}1& 0\\ 0& 1\\ & \end{array}\right]$, observe that the matrix has 2 rows and 2 columns, therefore, the dimension of matrix will be $2\times 2$.