Using properties of determinants, prove ...

Using properties of determinants, prove that :
`|{:((x+y)^(2),zx,xy),(zx,(z+y)^(2),xy),(zy,xy,(z+x)^(2)):}|=2xyz(x+y+z)^(3)`.

AI Generated Solution

DETERMINANTS
MODERN PUBLICATION|Exercise Examples (FREQUENCY ASKED QUESTIONS)|28 Videos
DETERMINANTS
MODERN PUBLICATION|Exercise Examples (QUESTIONS FROM NCERT EXAMPLAR|4 Videos
DETERMINANTS
MODERN PUBLICATION|Exercise Chapter test 4|12 Videos
CONTINUITY AND DIFFERENTIABILITY
MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos
DIFFERENTIAL EQUATIONS
MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

prove that: |(y^(2)z^(2),yz,y+z),(z^(2)x^(2),zx,z+x),(x^(2)y^(2),xy,x+y)|=0

Using the properties of determinants, show that: abs((x,x^2,yz),(y,y^2,xz),(z,z^2,xy))=(x−y)(y−z)(z−x)(xy+yz+zx)

By using properties of determinants.Show that: det[[x,x^(2),yzy,y^(2),zxz,z^(2),xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

Using properties of determinants,prove that [[-yz,y^(2)+yz,z^(2)+yzx^(2)+xz,-xz,z^(2)+xyx^(2)+xy,y^(2)+xy,-xy]]=(xy+yz+zx)^(2)

[[x,x^(2),yzy,y^(2),zxz,z^(2),xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

Prove the following : |(1,x,x^(2)-yz),(1,y,y^(2)-zx),(1,z,z^(2)-xy)|=0 .

(x-y-z)^(2)-(x^(2)+y^(2)+z^(2))=2(yz-zx-xy)

Determinant , form (x-y)(y-z)(z-x)(xy+yz+zx), of

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

|[1/x,1/y,1/z],[x^(2),y^(2),z^(2)],[yz,zx,xy]|