Using the properties of determinants ,show that

0 p-q p-r

q-p 0 q-r

r-p r-q 0

=0..

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Question

Using the properties of determinants ,show that
0 p-q p-r
q-p 0 q-r
r-p r-q 0
=0

Santosh Kumar · Accepted Answer

$[\begin{matrix} 0 & p - q & p - r \\ q - p & 0 & q - r \\ r - p & r - q & 0 \end{matrix}]$

R₁ → R₁ – R₃

$= [\begin{matrix} p - r & p - r & p - r \\ q - p & 0 & q - r \\ r - p & r - q & 0 \end{matrix}] = (p - r) [\begin{matrix} 1 & 1 & 1 \\ q - p & 0 & q - r \\ r - p & r - q & 0 \end{matrix}]$

R₂ → R₂ – R₃

$= (p - r) [\begin{matrix} 1 & 1 & 1 \\ q - r & q - r & q - r \\ r - p & r - q & 0 \end{matrix}] = (p - r) (q - r) [\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ r - p & r - q & 0 \end{matrix}] = 0$

(R₁ and R₂ are identical)

6

Using the properties of determinants ,show that 0 p-q p-r q-p 0 q-r r-p r-q 0 =0..

Using the properties of determinants ,show that

0 p-q p-r

q-p 0 q-r

r-p r-q 0

=0..