Chapter 11.3, Problem 3AYU

To determine

Whether the statement, “A determinate can never equal to zero” is true or false.

Answer to Problem 3AYU

The statement, “A determinate can never equal to zero” is false.

Explanation of Solution

Given information:

The statement, “A determinate can never equal to zero”.

Consider the provided statement, “A determinate can never equal to zero”.

Recall that the value of determinate only depends on its entries of rows and columns. So can be zero also. For example consider the following determinate,

  $D=\begin{array}{cc}2& 4\\ 1& 2\end{array}$

Since the above determinate have 2 rows ad 2 columns. Recall that to solve $2\times 2$ determinate first multiply entries of principal diagonal and then subtract other diagonal entries multiplication from it.

Now,

  $\begin{array}{c}D=\begin{array}{cc}2& 4\\ 1& 2\end{array}\\ =4-4\\ =0\end{array}$

So, the value of above determinate comes out to be zero.

Therefore, the statement, “A determinate can never equal to zero” is false.