If the system of equations `2x-3y+5z=12, 3x+y+lambdaz= mux7+y+8z=17` has infinitely many real solutions, then `lambda+mu`=

Options

A. 5
B. 3
C. 9
D. None of these

Answer

C

Explanation

`[A]B=[{:(1,-7,8),(2,-3,5),(3,1,lamda):}][{:(17),(12),(mu):}]`
`[A]B=[{:(1,-7,8,17),(0,11,-11,-22),(0,22,lamda-24,mu-51):}]` ltbgt `(R_(2)toR_(2)-2R_(1),R_(3)toR_(3)-3R_(1))`
`=[{:(1,17,8),(0,11,-11),(0,0,lamda-2):}{:(17),(-22),(lamda-7):}]`
For infinitley many solutions.
rank A=rank `[A|B]lt3`
`implieslamda-2=mu=0,mu-7=0`
`implieslamda+mu=9`