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Question: \[\left| \begin{matrix} 1 & a & b \\ - a & 1 & c \\ - b & - c & 1 \end{matrix} \right| =\]...

1 & a & b \\ - a & 1 & c \\ - b & - c & 1 \end{matrix} \right| =$$
A

1+a2+b2+c21 + a^{2} + b^{2} + c^{2}

B

1−a2+b2+c21 - a^{2} + b^{2} + c^{2}

C

1+a2+b2−c21 + a^{2} + b^{2} - c^{2}

D

1+a2−b2+c21 + a^{2} - b^{2} + c^{2}

Answer

1+a2+b2+c21 + a^{2} + b^{2} + c^{2}

Explanation

Solution

$\left| \begin{matrix} 1 & a & b \

  • a & 1 & c \
  • b & - c & 1 \end{matrix} \right| = 1(1 + c^{2}) - a( - a + bc) + b(ac + b)$

= 1+a2+b2+c21 + a^{2} + b^{2} + c^{2}.