Home
Class 12
MATHS
Using Cofactors of elements of third col...

Using Cofactors of elements of third column , evaluate , `Delta ={:|( 1,x,yz),(1,y,zx),( 1,z,xy) |:}`

Text Solution

Verified by Experts

The correct Answer is:
`(x-y)(y-z) (z-x) `
Promotional Banner

Similar Questions

Explore conceptually related problems

Using Cofactors of elements of second row, evaluate Delta ={:|( 5,3,8),( 2,0,1),( 1,2,3) |:}

Without expanding prove that Delta ={:|( x+y,y+z,z+x) ,( z,x,y),( 1,1,1) |:} =0

Find the minor and cofactors of all the elements of the determinants {:|( 1,-2),(4,3)|:}

Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y^2+1,yz),(xz,yz,z^2+1)|=1+x^2+y^2+z^2

The value of the determinant |{:(1 , x , x+ z) , (1 , y , z + x) , (1 , z , x + y):}| is

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

The element in the first row and third column of the inverse of the matrix [(1,2,-3),(0,1,2),(0,0,1)] is

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 .

Find the coordinates of the centroid fof the triangle whose vertices are (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3))

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