Q3. - Algebra 2

Question

Create a square matrix that does not have an inverse.

Step-by-Step Solution

Answer

The square matrix that does not have an inverse is: $\left[\begin{array}{cc}\mathbf{1}& \mathbf{2}\\ \mathbf{2}& \mathbf{4}\end{array}\right]$.

Step 1 ­- Description of step.

A square matrix is a matrix which has same number of rows and columns. 

Step 2 ­- Description of step.

A square matrix A does not have its inverse if$\left|A\right|=0$.

Therefore, to create a square matrix that does not have its inverse, create a matrix which is having it’s determinant as 0.

Step 3 ­- Description of step.

Consider the matrix $A$as $\left[\begin{array}{cc}1& 2\\ 2& 4\end{array}\right]$.

Notice that:

$\begin{array}{c}\left|\begin{array}{cc}1& 2\\ 2& 4\end{array}\right|=\left(1\right)\left(4\right)-\left(2\right)\left(2\right)\\ =4-4\\ =0\end{array}$

As, $\left|A\right|=0$, therefore the matrix $A$ will not have an inverse.

Therefore, the square matrix that does not have an inverse is: $\left[\begin{array}{cc}1& 2\\ 2& 4\end{array}\right]$.