consider the following system of linear equations:

\(5x+8y-6z=14\)

\(3x+4y-2z=8\)

\(x+2y-2z=3\)

convert into augmented matrix

\([(5,8,-6,|,14),(3,4,-2,|,8),(1,2,-2,|,3)]\)

Transform the above matrix into reduced row echelon form

\(R_2\Rightarrow\frac{5}{3} R_2-R_1\)

\(R_3\Rightarrow5R_3-R_1\)

\([(5,8,-6,|,14),(0,-\frac{4}{3},-\frac{8}{3},|,-\frac{2}{3}),(0,2,-4,|,1)]\)

\(R_3\Rightarrow(\frac{2}{3})R_3+R_2\)

\([(5,8,-6,|,14),(0,-\frac{4}{3},-\frac{8}{3},|,-\frac{2}{3}),(0,0,0,|,0)]\)

Hence, solution of a system of linear equations does not exist