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using properties of determinats show that det(b 2 +c 2 a 2 a 2 ,b 2 c 2 +a 2 b 2 ,c 2 c 2 a 2 +b 2 )=4a 2 b 2 c 2

using properties of determinats show that det(b2+c2  a2  a2,b2  c2+a2  b2,c2 c2 a2+b2)=4a2b2c2

Grade:12th pass

1 Answers

mycroft holmes
272 Points
7 years ago
Using R1 \rightarrow R1-R2-R3 and taking 2 common out of R1, -2 \begin{vmatrix} 0& c^2& b^2\\ b^2& c^2+a^2 & b^2 \\ c^2& c^2& a^2+b^2 \end{vmatrix}
 
Now use R2 \rightarrow R2-R1 and R3\rightarrowR3-R1 to obtain
-2 \begin{vmatrix} 0& c^2& b^2\\ b^2& c^2 & 0 \\ c^2& 0& a^2 \end{vmatrix}
and now expand from R1 to easily get the value as 4a^2b^2c^2

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