The values of λ  and μ  for which the system of equations x+y+z=6 , x+2y+3z=10 , x+2y+λz=μ  has infinitely many solutions are

The given system is of the form AX=B , whereA=11112312λ, X=xyz  and B=610μFor infinitely many solutions|A|=0,   6111023μ2λ=0 16111031μλ=0  and also  116121012μ=0⇒λ−3=0 , 2λ+μ−16=0⇒10λ−3μ−6(λ−3)+(μ−10)=0  and μ−10=0⇒λ−3=0, 2(λ−3)+(μ−10)=0⇒4(λ−3)−2(μ−10)=0And μ−10=0⇒λ=3  and μ=10 .