Write a system of equations that cannot be solved using Cramer’s Rule.

The formation of equations that returns the main determinant as 0 can be used.

Form the equations in such a manner so that the determinant that is in denominator of each variable is equal to 0.

$\begin{array}{c}2m-n+3o=5\\ 3m+2n-5o=4\\ m-4y+11z=3\end{array}$

Use Cramer’s rule for the variable m.

$m=\frac{\left|\begin{array}{ccc}j& b& c\\ k& e& f\\ l& h& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$

Use the provided equations and substitute the value of a, b, c, d, e, f, g,

h, i, j, k and l into$m=\frac{\left|\begin{array}{ccc}j& b& c\\ k& e& f\\ l& h& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$after it perform simplification of

determinants to write the value of m.

$\begin{array}{c}m=\frac{\left|\begin{array}{ccc}5& -1& 3\\ 4& 2& -5\\ 3& -4& 11\end{array}\right|}{\left|\begin{array}{ccc}2& -1& 3\\ 3& 2& -5\\ 1& -4& 11\end{array}\right|}\\ =\frac{3}{0}\end{array}$

The denominator of the value of m is 0 which means that the main determinant is 0 so each value will be infinite.

As the solution represents that each variable has infinite value which means that the obtained system of equations cannot be solved with the help of Cramer’s rule.