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KCET2011MathematicsMatrices

If [ array ccr 1 & 2 & -1 1 & x-2 & 1 x & 1 & 1 array ] is singular, then the value of x is

Options

  1. A2
  2. B3
  3. C1
  4. D0

Correct answer

A. 2

Step-by-step solution

Let A= [ array ccc 1 & 2 & -1 1 & x-2 & 1 x & 1 & 1 array ] if the matrix A is singular, then |A|=0 | array ccc 1 & 2 & -1 1 & x-2 & 1 x & 1 & 1 array |=0 Expand with respect to R₁ 1(x-2-1)-2(1-x)-1 (1-x²+2 x )=0 x-3-2+2 x-1+x²-2 x=0 x²+x-6=0 (x-2)(x+3)=0 x=2,-3

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