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CUET
-- Mathematics - Section A
Determinants
Choose the correct value for |(x+y)2zxzyzx(z+y)2xyzyxy(z+x)2| |
2(x+y+z)3 2xyz(x+y+z)3 xyz(x+y+z)3 2xyz(x+y+z)2 |
2xyz(x+y+z)3 |
Given, |(x+y)2zxzyzx(z+y)2xyzyxy(z+x)2| Applying, R1→zR1,R2→xR2,R3→yR3, we get =1xyz|z(x+y)2z2xz2yzx2x(z+y)2x2yzy2xy2y(z+x)2| Applying, C1→C1z,C2→C2x,C3→C3y we get =|(x+y)2z2z2x2(z+y)2x2y2y2(z+x)2| Applying, C1→C1−C3,C2→C2−C3 we get =(x+y+z)2|x+y−z0z20z+y−xx2y−z−xy−z−x(z+x)2| Applying, C1→C1+C3z,C2→C2+C3x we get =(x+y+z)2|x+yz2xz2x2zz+yx2002xz| =(x+y+z)2[2xz(xz+xy+yz+y2−zx)] =(x+y+z)2[2xyz(x+y+z)] =2xyz(x+y+z)3 |