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COMEDK2014MathematicsMatrices

If [ array cc -2 & 5 3 & -1 array ] [ array l x y array ]= [ array cc 1 & 2 3 & 4 array ] [ array c 3 -1 array ] , then (x, y) is

Options

  1. A(1,2)
  2. B(-1,2
  3. C(1,-2
  4. D(2,1)

Correct answer

D. (2,1)

Step-by-step solution

[ array cc -2 & 5 3 & -1 array ]_ 2 x 2 [ array l x y array ]_ 2 1 = [ array cc 1 & 2 3 & 4 array ]_ 2 2 [ array c 3 -1 array ]_ 2 1 [ array c -2 x+5 y 3 x-y array ]= [ array l 1 5 array ] -2 x+5 y=1,3 x-y=5 or y=3 x-5 ...(i) -2 x+5(3 x-5)=1 -2 x+15 x-25=1 13 x=26 x=2 Substituting x=2 in Eq. (i), we get y=6-5=1 Hence, (x, y)=(2,1)

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