Question

If x+y+z=0,x+ay+z=0,ax+by+z=0, has no solution then value of b can be

Answer 1

$final \: result \: = b \: belongs \: to \: \\ real \: number \: and \: a \: not \: equal \: to \: \\ b \: not \: equal \: to \: 1\\ \\ concepts \: used \: \\ 1)if \: system \: \: of \: \: linear \: equation \: \\ has \: no \: solution \: then \: determinant \\ of \: coefficent \: matrix \: is \: 0. \\ \\ \\ \: \\ calculation \: process \\ 1) \: det erminant \: of \: coefficent \: \\ matrix \: = 0 \: gives \: \: a = 0 \: or \: 2 \\ this \: i \:s \: independent \: of \: b \: . \\ 2)a \: not \: equal \: to \: b \: not \: equal \: to \: 1 \: \\ implies \: \: these \: \: linear \: equations \\ \:does \: not \: give \: infinitely \: many \\ solutions. \\ hope \: you \: understand \: my \: answer.$

Answer 2

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.