Question

Write a matrix whose determinant is zero.

Short answer

A matrix whose determinant is zero $\left[\begin{array}{cc}-3& -6\\ 2& 4\end{array}\right]$.

Step-by-step solution

- Define the determinant of second-order matrix

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-bc$.

- Find the Matrix

Let a matrix whose determinant is zero be $\left[\begin{array}{cc}-3& -6\\ 2& 4\end{array}\right]$. Then,

$\left|\begin{array}{cc}-3& -6\\ 2& 4\end{array}\right|=-3\times \left(4\right)-\left(-6\right)\left(2\right)$

- Simplify

To further verify simplify by multiplying the values first.

$\begin{array}{c}\left|\begin{array}{cc}-3& -6\\ 2& 4\end{array}\right|=-3\times \left(4\right)-\left(-6\right)\left(2\right)\\ =-\text{12}+12\\ =\text{0}\end{array}$

Hence, verified. A matrix whose determinant is zero is $\left[\begin{array}{cc}-3& -6\\ 2& 4\end{array}\right]$.