determinants.....

\hspace{-16}$Show that $\mathbf{\begin{vmatrix} a^2+b^2+c^2 &bc+ca+ab &bc+ca+ab \\\\ bc+ca+ab &a^2+b^2+c^2 &bc+ca+ab \\\\ bc+ca+ab &bc+ca+ab & a^2+b^2+c^2 \end{vmatrix}}$\\\\\\ is always Positive \;, Where $\mathbf{a\;,b\;,c}$ are distinct real no.

5 Answers

1
Abhinav Gupta ·

Can it be zero too?

1
Abhinav Gupta ·

Clearly it can be zero too.

341
Hari Shankar ·

it equals (a3+b3+c3-3abc)2.So non-negative

21
Shubhodip ·

That proves that it is closed under multiplication...

1708
man111 singh ·

Thanks bhatt Sir and abhinav and Subhodip

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