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Question: If \|A\| = \(\left| \begin{matrix} a & b & c \\ x & y & z \\ p & q & r \end{matrix} \right|\) & \|B\...

If |A| = ∣abcxyzpqr∣\left| \begin{matrix} a & b & c \\ x & y & z \\ p & q & r \end{matrix} \right| & |B| = $\left| \begin{matrix} q & - b & y \

  • p & a & - x \ r & - c & z \end{matrix} \right|$
A

|A| = 2|B|

B

|A| = |B|

C

|A| = –|B|

D

None

Answer

|A| = –|B|

Explanation

Solution

$\left| \begin{matrix} q & - p & r \

  • b & a & - c \ y & - x & z \end{matrix} \right|=– = –\left| \begin{matrix}
  • p & q & r \ a & - b & - c \
  • x & y & z \end{matrix} \right|$

= – $\left| \begin{matrix} a & - b & - c \

  • x & y & z \
  • p & q & r \end{matrix} \right|=–(–1)= – (–1) \left| \begin{matrix}
  • a & b & c \
  • x & y & z \
  • p & q & r \end{matrix} \right|$

= –∣abcxyzpqr∣\left| \begin{matrix} a & b & c \\ x & y & z \\ p & q & r \end{matrix} \right| = –|A|