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| array ccc a & b & c a^2 & b^2 & c^2 1 & 1 & 1 array | is not equal to

Options

  1. A| array ccc a+1 & b+1 & c+1 a^2+1 & b^2+1 & c^2+1 1 & 1 & 1 array |
  2. B| array ccc a-b & b-c & c a^2-b^2 & b^2-c^2 & c^2 0 & 0 & 1 array |
  3. C| array ccc a(a+1) & b(b+1) & c(c+1) a+1 & b+1 & c+1 -1 & -1 & -1 array |
  4. D| array ccc a+b & b+c & c+a a^2+b^2 & b^2+c^2 & c^2+a^2 2 & 2 & 2 array |

Correct answer

D. | array ccc a+b & b+c & c+a a^2+b^2 & b^2+c^2 & c^2+a^2 2 & 2 & 2 array |

Step-by-step solution

| array ccc a & b & c a^2 & b^2 & c^2 1 & 1 & 1 array |= | array ccc a+1 & b+1 & c+1 a^2+1 & b^2+1 & c^2+1 1 & 1 & 1 array | aligned & R ₁ R ₁+ R ₃, R ₂ R ₂+ R ₃ & | array ccc a & b & c a^2 & b^2 & c^2 1 & 1 & 1 array |= | array ccc a-b & b-c & c a^2-b^2 & b^2-c^2 & c^2 0 & 0 & 1 array | & C ₁ C ₁- C ₂, C ₂ C ₂- C ₃ & | array ccc a & b & c a^2 & b^2 & c^2 1 & 1 & 1 array | & =- | array ccc a^2 & b^2 & c^2 a & b & c 1 & 1 & 1 array |=- | array ccc a^2+a & b^2+b & c^2+c a+1 & b+1 & c+1 1 & 1 & 1 array | & = | array c

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