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For what values of $a, b$ the system of equations $x+y+z=3, x+2y+2z=6, x+ay+3z=b$ have no solution 

  1. $a=3, b=9$
  2. $a=3, b\neq9$
  3. $a\neq 3, b \in \mathbb{R}$
  4. $a=3, b \in \mathbb{R}$
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A martix has no soln when → $ {(Adj A).B} / |A|$   = x / 0 as answer. where x CANNOT be 0, If x=0 then we can have ininite solutions

|A| = Co-efficients of the variables of the equation

|A|=

Now |A| = 0 only when a=3.

And (Adj A) =

and B = Values on the RHS of the equations

B=

Now ( Adj A). B is NOT 0 when b=9 but it becomes 0 when b = 6. Now as 6 ϵ R so, b ϵ R is  NOT POSSIBLE.

So ans is A. a=3, b=9

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