Determinants - Past JEE Questions - Problems

1. The system of equations

λx+y+z = 0
-x+λy+z = 0
-x-y+λz = 0

will have a non-zero solution if real values of λ are given by(or if real values of λ are equal to) ________________________ .
(JEE 1984 Scr)

2. State whether the statement is true or false.

If
determinant

|x1 y1 1|
|x2 y2 1|
|x3 y3 1|

is equal to determinant

|a1 b1 1|
|a2 b2 1|
|a3 b3 1|

then the two triangles with vertices 9x1,y1), (x2,y2), (x3,y3) and (a1,b1), (a2,b2) and (a3,b3) must be congruent.