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AP EAMCET20225 Jul 2022Morning ShiftMathematicsMatricesActual

Let G(x)= [ array ccc x & - x & 0 x & x & 0 0 & 0 & 1 array ] . If x+y=0 , then G(x) G(y)=

Options

  1. Anull Matrix
  2. Bskew-symmetric Matrix
  3. Cidentity Matrix
  4. Dsymmetric Matrix

Correct answer

C. identity Matrix

Step-by-step solution

Here, G(x)= [ array ccc x & - x & 0 x & x & 0 0 & 0 & 1 array ]G(y)= [ array ccc y & - y & 0 y & y & 0 0 & 0 & 1 array ] So, x+y=0 y=(-x) Now, G(-x)= [ array ccc (-x) & - (-x) & 0 (-x) & (-x) & 0 0 & 0 & 1 array ]G(x) G(y)= [ array ccc x & - x & 0 x & x & 0 0 & 0 & 1 array ] [ array ccc x & x & 0 - x & x & 0 0 & 0 & 1 array ]= [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ]=I

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