Question

If 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:

an empty set
an infinite set
a finite set containing two or more elements
a singleton

Answer 1

Answer:

♠ The correct option is D.

Explanation:

Here,

For a = 1, the equations become

x + y + z = 1

x + y + z = 1

x + by + z = 0

These equations give no solution for b = 1

Therefore, S is singleton set.

Answer 2

Answer:

Explanation:

These three equations will have no solution if derterminant of these equations is 0.

∴Δ= 111

1a1 =0

ab1

⇒a−b+a−1+b−a2=0

⇒−(a−1)2=0

⇒a=1

If we put, a=1,

Eqaution (2) and (1), will become same.

Now, if we put b=1 in third equation, then it will become parallel to first two equations.

So, for this system to have no solutions, b should be 1.

Thus, S is a singleton set containing one element 1.