Home
Class 12
MATHS
[[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]...

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

Promotional Banner

Topper's Solved these Questions

  • II PUC TOPPER'S ANSWERS MARCH (2017)

    OSWAAL PUBLICATION|Exercise PART - D Answer any six questions :|11 Videos

  • II PUC TOPPER ANSWERS MARCH-2016

    OSWAAL PUBLICATION|Exercise PART - E|2 Videos

  • INTEGRALS

    OSWAAL PUBLICATION|Exercise DEFINITE INTEGRALS (LONG TYPE ANSWER TYPE QUESTIONS - III)|40 Videos

Similar Questions

Explore conceptually related problems

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

Show that |(x,x^(2),yz),(y,y^(2),zx),(z,z^(2),xy)|=(x-y)(y-z)(z-x)(xy+yz+zx)

|[1, x, x^2 ],[1, y, y^2],[1, z, z^2]|=

|[x,1,y+z],[y,1,z+x],[z,1,x+y]|=

|(x, 4, y+z),(y, 4, z+x),(z, 4, x+y)|=

Add: 2x(z-x-y) and 2y(z-y-x)

using properties of determinant prove that {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

Delta= |[Ax,x^(2),1],[By,y^(2),1],[Cz, z^(2),1]| and Delta_(1)= |[A,B,C],[x,y,z],[zy, zx,xy]|

Prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|= 2(x+y+z)^(3)

Prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|= 2(x+y+z)^(3)