Question 21

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Jambmaths question: 

A matrix $P=\left( \begin{matrix}   a & b  \\   c & d  \\\end{matrix} \right)$is such that PT = -P. PT is the transpose of P. If b = 1, then P is

Option A: 

$\left( \begin{matrix}   0 & 1  \\   1 & 0  \\\end{matrix} \right)$

Option B: 

$\left( \begin{matrix}   0 & 1  \\   -1 & 0  \\\end{matrix} \right)$

Option C: 

$\left( \begin{matrix}   0 & 1  \\   -1 & 1  \\\end{matrix} \right)$

Option D: 

$\left( \begin{matrix}   1 & 1  \\   -1 & 0  \\\end{matrix} \right)$

Jamb Maths Solution: 

Note: A skew – symmetric matrix is such that

PT = –P. Major Characteristics of a skew –symmetric matrix is that

  1. Elements along the principal (or main) diagonal are zeros and
  2. Sum of the diagonal element will give zero.

Follow this condition, option B is the correct option has it satisfy this condition.

You can test this

  1. The elements along the principal diagonal are 0, 0,
  2. The sum of 1 and –1 is zero.
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