Consider the following system of linear equations.

3x2y+z=4

x+yz=2

x+z=1

(i) Write the system in the formAx=b.

(ii) Use the determinant to show thatAis invertible.

(iii) Find the inverse ofAusing the Gauss-Jordan elimination.

(iv) Find the inverse ofAusing the determinant and the adjoint ofA, i.e.,A1=1det(A)adj(A).

(v) Comment on your answers in part (iii) and (iv).

(vi) Solve the system using the inverse matrix found in part (iv).