Question

It S is the set of distinct values of ‘b’ for which the following system of linear equations
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is :
(1) an empty set
(2) an infinite set
(3) a finite set containing two or more elements
(4) a singleton

Answer 1

=> a = 1

For a = 1 we have first two planes co-incident

x + y + z = 1
ax + by + z = 0
For no solution these two are parallel

1/a = 1/b 1/1
=> a = 1 , b = 1