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Question: If A is a 3 × 3 skew-symmetric matrix, then \|A\| is given by –...

If A is a 3 × 3 skew-symmetric matrix, then |A| is given by –

A

0

B

–1

C

1

D

None of these

Answer

0

Explanation

Solution

Let A = $\begin{pmatrix} 0 & a & b \

  • a & 0 & c \
  • b & - c & 0 \end{pmatrix}bethegivenskewsymmetricmatrix.Wehave∥A∥=be the given skew symmetric matrix. We have \|A\| = \begin{pmatrix} 0 & a & b \
  • a & 0 & c \
  • b & - c & 0 \end{pmatrix}==\left| \begin{matrix} 0 & - a & - b \ a & 0 & - c \ b & c & 0 \end{matrix} \right|$

[Q |A| = |A¢|] = (–1)3 $\left| \begin{matrix} 0 & a & b \

  • a & 0 & c \
  • b & - c & 0 \end{matrix} \right|$ = – |A|

Ž 2 |A| = 0 Ž |A| = 0.