For what values of k, the system of linear equations

has a unique solution?

Let us write the given system of linear equation in Matrix form.

⇒ A =

For solution to be unique |A| ≠ 0

∴ ≠ 0

= 1(k - ( - 2)) - 1(2k - ( - 3)) + 1(4 - 3)

= k + 2 - 2k - 3 + 1

= - k≠ 0.

For every value expect 0, this system has unique solution.