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

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:

MARKS Content Team · Accepted Answer

Correct answer: (D) A singleton. For no solution D= 1 1 1 1 a 1 a b 1 =0 Expanding the determinant along the first row, we get D=-a-1^2=0 ⇒ a=1 For a=1, first two planes are coincident. Now, we have x+y+z=1 & ax+by+z=0 For no solution, these two planes are parallel. ⇒1/a=1/b=1/1 ⇒a=1 & b=1. ∴ b=1 ⇒ it is a singleton set

If $S$ is the set of distinct values of $b$ for which the following system of linear equations

$x + y + z = 1$

$x + a y + z = 1$

$a x + b y + z = 0$

has no solution, then $S$ is:

Solution

Relevant Questions

If S is the set of distinct values of b for which the following system of linear equationsx+y+z=1x+ay+z=1ax+by+z=0has no solution, then S is:

Solution

Relevant Questions

If $S$ is the set of distinct values of $b$ for which the following system of linear equations

$x + y + z = 1$

$x + a y + z = 1$

$a x + b y + z = 0$

has no solution, then $S$ is: