|[a-b,p-q,x-y],[b-c,q-r,y-z],[c-a,r-p,z-x]|=

" 1."|[a-b,b-c,c-a],[x-y,y-z,z-x],[p-q,q-r,r-p]|" is equal to "

Without expanding the determinant prove the following. |[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 , prove that: |[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]|

If |[a, p, x],[ b, q, y], [c, r, z]|=16 , then the value of |[p+x, a+x, a+p], [q+y ,b+y, b+q],[ r+z, c+z, c+r]| is (a) 4 (b) 8 (c) 16 (d) 32

If |[a, p, x],[ b, q, y], [c, r, z]|=16 , then the value of |[p+x, a+x, a+p], [q+y ,b+y, b+q],[ x+z, c+z, c+r]| is 4 (b) 8 (c) 16 (d) 32

Evaluate the following determinants: [[a-b,b-c,c-a],[x-y,y-z,z-x],[p-q,q-r,r-p]]

Using the property of determinants and without expanding, prove that: |[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]|

If |[p,q-y,r-z],[p-x,q,r-z],[p-x,q-y,r]|=0 find the value of p/x+q/y+r/z

If |[p,q-y,r-z],[p-x,q,r-z],[p-x,q-y,r]|=0 find the value of p/x+q/y+r/z

Prove that the value of each the following determinants is zero: |[a-b,b-c,c-a],[ x-y, y-z, z-x],[ p-q, q-r ,r-p]|