Let `A={X=(x, y, z)^(T): PX=0" and "x^(2)+y^(2)+z^(2)=1}`, where `P=[(1,2,1),(-2,3,-4),(1,9,-1)]`, then the set A:

Use product {:[( 1,-1,2),( 0,2,-3),( 3,-2,4) ]:} {:[( -2,0,1),(9,2,-3),(6,1,-2) ]:} to solve the system of equations x-y+2z=1 2y-3z=1 3x-2y+4z =2

Use product {:[( 1,-1,2),( 0,2,-3),( 3,-2,4) ]:} {:[( -2,0,1),(9,2,-3),(6,1,-2) ]:} to solve the system of equations x-y+2z=1 2y-3z=1 3x-2y+4z =2

If x, y, z are all distinct and |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 then value of x y z is :

{:|( 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 .

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 .

Let matrix A=[{:(x,y,-z),(1,2,3),(1,1,2):}] , where x,y,z in N . If |adj(adj(adj(adjA)))|=4^(8)*5^(16) , then the number of such (x,y,z) are

Let matrix A=[{:(x,y,-z),(1,2,3),(1,1,2):}] , where x,y,z in N . If |adj(adj(adj(adjA)))|=4^(8)*5^(16) , then the number of such (x,y,z) are

Let matrix A=[{:(x,y,-z),(1,2,3),(1,1,2):}] , where x,y,z in N . If |adj(adj(adj(adjA)))|=4^(8)*5^(16) , then the number of such (x,y,z) are

Let matrix A=[{:(x,y,-z),(1,2,3),(1,1,2):}] , where x,y,z in N . If |adj(adj(adj(adjA)))|=4^(8)*5^(16) , then the number of such (x,y,z) are

If (x_(1),y_(1),z_(1)) , (x_(2),y_(2),z_(2)) , (x_(3) ,y_(3),z_(3)) and (x_(4) , y_(4) , z_(4)) be the consecutive vertices of a parallelogram, show that x_(1)+x_(3)=x_(2)+x_(4),y_(1)+y_(3)=y_(2)+y_(4) and z_(1)+z_(3)=z_(2)+z_(4) .