| a^2+b^2/c c c | | a b2+c2/a a | |b b c2+a2/b| - Maths - Determinants

Question

| a^2+b^2/c c c |
| a b2+c2/a a |
|b b c2+a2/b|

Priyanka Kedia · Accepted Answer

Let Δ=a2+b2cccab2+c2aabbc2+a2bMultiply R1,R2, and R3 by c,a, and b respectively and hence divide Δ by abc, we have,Δ=1abca2+b2c2c2a2b2+c2a2b2b2c2+a2  =1abc0-2b2-2a2a2b2+c2a2b2b2c2+a2                     R1→R1-R2+R3  =-2abc0b2a2a2b2+c2a2b2b2c2+a2  =-2abc0b2a2a2c20b20c2                        R2→R2-R1 and R3→R3-R1  =-2abc0-b2a2c2-0+a20-b2c2  =-2abc-2a2b2c2  =4abcHence, Δ=4abc