The given system of equations is :-

2x + y – z = 7

x – 3y + 2z = 1

x + 4y – 3z = 5

The matrix equation corresponding to the above system is

Let A = and B =

|A| = = 2(9-8) -1(-3-2) -1(4+3) = 2+5-7 = 0

and adjA =

(adjA)B = = 0

So, No solution exists.