The values of λ and μ such that the system of equations x + y + z = 6 , 3 x + 5 y + 5 z = 26 and x + 2 y + λ z = μ has no solution, are:

Step-by-step solution

For the system of equations a 1 x + b 1 y + c 1 z = d 1 ,   a 2 x + b 2 y + c 2 z = d 2 and a 3 x + b 3 y + c 3 z = d 3 , We have D = a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 ,   D x = d 1 b 1 c 1 d 2 b 2 c 2 d 3 b 3 c 3 ,   D y = a 1 d 1 c 1 a 2 d 2 c 2 a 3 d 3 c 3 and D z = a 1 b 1 d 1 a 2 b 2 d 2 a 3 b 3 d 3 . And, the system has no solution, if D = 0 and atleast one of D x ,   D y   &   D z is non-zero. Thus, for the given system of equations, x + y + z = 6 , 3 x + 5 y + 5 z = 26 an