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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
If $a,b,c$ are distinct and rational numbers then $\left| {\begin{array}{*{20}{c}}
{\left( {{a^2} + {b^2} + {c^2}} \right)}&{ab + bc + ca}&{ab + bc + ca}\\
{ab + bc + ca}&{\left( {{a^2} + {b^2} + {c^2}} \right)}&{\left( {bc + ca + ab} \right)}\\
{ab + bc + ca}&{\left( {ab + bc + ca} \right)}&{\left( {{a^2} + {b^2} + {c^2}} \right)}
\end{array}} \right|$ is always 
  • A
    zero
  • ✓
    Rational $\&$ Positive
  • C
    Rational $\&$ Negative
  • D
    Irrational and Positive
✓

Answer

Correct option: B.
Rational $\&$ Positive
b
$\left|\begin{array}{lll}{a} & {b} & {c} \\ {b} & {c} & {a} \\ {c} & {a} & {b}\end{array}\right|\left|\begin{array}{lll}{a} & {b} & {c} \\ {b} & {c} & {a} \\ {c} & {a} & {b}\end{array}\right|$

$=\left|\begin{array}{lll}{a} & {b} & {c} \\ {b} & {c} & {a} \\ {c} & {a} & {b}\end{array}\right|^{2}=$ Rational and Positive

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