show that the determinant of (A) is 4a2b2c2 where in (A) a11= b2+c2 ,a12=ab , a13=ac a21=ba ,a22=c2+a2, a23=bc a31=ca - Maths - Determinants

Question

show that the determinant of (A) is
4a2b2c2 where in (A)
a11 = b2+c2 ,a12=ab
, a13=ac
a21=ba ,a22=c2+a2,
a23=bc
a31=ca ,a32=cb,
a33=a2+b2

Anuradha Sharma · Accepted Answer

A=b2+c2abacbaa2+c2bccacbb2+a2So A=b2+c2abacbaa2+c2bccacbb2+a2Now
multiplying and dividing R1 by a R2 by b and R3 by c we get,
=1abcab2+c2a2ba2cb2aba2+c2b2cc2ac2bcb2+a2Now taking a, b, c common
from C1, C2 and C3 we get, =abcabcb2+c2a2a2b2a2+c2b2c2c2b2+a2Now
applying
R1→R1-(R2+R3)=0-2c2-2b2b2a2+c2b2c2c2b2+a2=-20c2b2b2a2+c2b2c2c2b2+a2Now
applying C3→C3-C1=-20c2b2b2a2+c20c2c2b2+a2-c2Now expanding
along R1 we get,
=-20-c2a2+c2b2+a2-c2+b2b2c2-c2a2-c4=2c2a2+c2b2+a2-c2-2b2b2c2-c2a2-c4=2c2a2+2c4b2+a2-c2-2b4c2+2b2c2a2+2b2c4=4a2b2c2

show that the determinant of (A) is 4a2b2c2 where in (A) a11 = b2+c2 ,a12=ab , a13=ac a21=ba ,a22=c2+a2, a23=bc a31=ca ,a32=cb, a33=a2+b2

show that the determinant of (A) is 4a²b²c²where in (A)

a₁₁ = b²+c²,a₁₂=ab , a₁₃=ac

a₂₁=ba ,a₂₂=c²+a², a₂₃=bc

a₃₁=ca ,a₃₂=cb, a₃₃=a²+b²