The values of λ and μ for which the system of linear equations x+y+z=2x+2y+3z=5x+3y+λz=μhas infinitely many solutions are, respectively :

x+y+z=2(1)x+2y+3z=5(2) has infinitely - many solutions x+3y+λz=m (2) -( 1) gives y+2z=3  →(4) hasinfinitely - many solutions (3)-(2) gives y+(λ-3)z=μ-5  →(5)}⇒11=λ-32=μ-53⇒λ=5 and μ=8