[" A is symmetric matrix."],[" Ithout expending prove that "[[o,p-q,p-r],[q-p,o,q-r],[r-p,r-q,o]]=0]

|(0,p-q,p-r),(q-p,0,q-r),(r-p,r-q,0)|=

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

Without expanding the determinant prove that: |(0, p-q, p-r), (q-p,0, q-r),(r-p, r-q, 0)|=0

Without expanding the determinant prove that: {:|(0,p-q,p-r),( q-p,0, q-r),(r-p,r-q,0)|:}=0

p,q,q,r Show that ,q,p,,q,r,r,p,r,q

Show that: |[p-q-r,2p,2p],[2q,q-r-p,2q],[2r,2r,r-p-q]|=(p+q+r)^3

If p,q and r are in AP,then prove that (p+2q-r)(2q+r-p)(r+p-q)=4pqr

Without expanding at any stage, prove that |(p+q, q+r, r+p),(q+r, r+p, p+q),(r+p, p+q, q+r)| = 2|(p,q,r),(q,r,p),(r,p,q)| .

If a,b,c are respectively the sums of p,q,r terms of an A.P., prove that a/p(q-r)+b/q(r-p)+c/r(p-q)=0