If det [ p b c

a q c = 0 then find (p/p-a) + (q/q-b) + (r/r-c)

a b r]

the given determinant is:
paabqbccr=0
‚Äčapplying R1R1-R3 and R2R2-R3p-a0a0q-bbc-rc-rr=0taking common (p-a) from C1 ; (q-b) from C2 and (c-r) from C3(p-a)(q-b)(c-r)10ap-a01bq-b11rc-r=0
since p, q, r and a, b , c are different numbers
10ap-a01bq-b11rc-r=0
expanding the determinant:
rc-r-bq-b+0+1*0-ap-a=0rc-r-bq-b-ap-a=0-rr-c-bq-b-ap-a=0rr-c+bq-b+ap-a=0
adding 2 on the both sides:
rr-c+bq-b+1+ap-a+1=2rr-c+b+q-bq-b+a+p-ap-a=2rr-c+qq-b+pp-a=2

hope this helps you
 

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