[0,p-q,p-r,],[q-p,0,q-r,],[r-p,r-q,0,],[[" (a) "p+q+r," (b) "p+q-r],[" (c) "1,," (d) "0]]

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

Without expanding at any stage, prove that the value of each of the following determinants is zero. (1) |[0,p-q,p-r],[q-p,0,q-r],[r-p,r-q,0]| (2) |[41,1,5],[79,7,9],[29,5,3]| (3) |[1,w,w^2],[w,w^2,1],[w^2,1,w]| , where w is cube root of unity

Without expanding at any stage, prove that the value of each of the following determinants is zero. (1) |[0,p-q,p-r],[q-p,0,q-r],[r-p,r-q,0]| (2) |[41,1,5],[79,7,9],[29,5,3]| (3) |[1,w,w^2],[w,w^2,1],[w^2,1,w]| , where w is cube root of unity

Without expanding at any stage, prove that the value of each of the following determinants is zero. (1) |[0,p-q,p-r],[q-p,0,q-r],[r-p,r-q,0]| (2) |[41,1,5],[79,7,9],[29,5,3]| (3) |[1,w,w^2],[w,w^2,1],[w^2,1,w]| , where w is cube root of unity

Without expanding at any stage, prove that the value of each of the following determinants is zero. (1) |[0,p-q,p-r],[q-p,0,q-r],[r-p,r-q,0]| (2)|[41,1,5],[79,7,9],[29,5,3]| (3)|[1,w,w^2],[w,w^2,1],[w^2,1,w]| , where w is cube root of unity

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

Choose the correct answer from the bracket.The value of the determinant abs[[0,p-q,p-r],[q-p,0,q-r],[r-p,r-q,0]] is

Add: p ( p – q), q ( q – r) and r ( r – p)