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if S is the set of distinct values of b for which the following set of linear equations has no solution,then S is x+Y+z=1 x+ay+z=1 ax+by+z=0 answer-empty set .how?please explain

if S is the set of distinct values of b for which the following set of linear equations has no solution,then S is
x+Y+z=1
x+ay+z=1
ax+by+z=0
answer-empty set .how?please explain
 

Grade:12

1 Answers

Arun
25763 Points
3 years ago

Here,

             1     1     1

D =       1     a      1       = 0

              a      b      1

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 or empty set

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