Using the property of determinants and without expanding ` {:|( b+c,q+r,y+z),( c+a,r+p,z+x),( a+b,p+q,x+y) |:}=2 {:|(a,p,x),( b,q,y),(c,r,z)|:}`

|(b+c, q+r, y+z),(c+a,r+p,z +x),(a+b,p+q,x+y)|=2|(a,p,x),(b,q,y),(c,r,z)|

Using the property of determinants and without expanding {:|( x,a,x+a),( y,b,y+b),(z,c,z+c)|:} =0

|(x,a,x+a),(y,b,y+b),(z,c,z+c)| = 0

Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,r+p,p+q),(y+z,z+x,x+y)|=2{:|(a,b,c),(p,q,r),(x,y,z)|

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

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 .

[[ 0 , p-q , p-r ],[q-p , 0 , q-r],[ r-p , r-q , 0 ]] =

If [[ p , q-y , r-z],[ p-x , q , r-z ],[ p-x , q-y , r ]]=0 , then (p)/(x)+(q)/(y)+(r)/(z)=

In the adjacent figure, find the value of x, y, z and a, b, c.

If P ={ a, b, c} and Q = {r} , find P xx Q .