If `A=[[0,q,r],[p,(a-b),(b-c)], [0,0,(c-b)]]` then find `|A|`

If a!=p ,b!=q ,c!=r and |[p, b, c ],[a, q, c ],[a ,b, r]|=0, then find the value of p/(p-a)+q/(q-b)+r/(r-c)dot

Let a_r=r(.^7C_r),b_r=(7-r)(.^7C_r) and A_r=[(a_r,0),(0,b_r)] . If A=sum_(r=0)^7 A_r=[(a,0),(0,b)] , then find the value of a+b .

If /_\=|(0,c,b),(c,0,a),(b,a,0)|, then /_\=

Given A=[{:(,3,0),(,0,4):}], B=[{:(,a,b),(,0,c):}] and AB=A+B, find the values of a,b and c.

If A=|[a, b, c],[ x, y, z],[ p, q, r]| and B=|[q, -b, y],[ -p, a, -x],[ r,-c, z]| , without expanding or evaluating A and B , show that A+B=0 .

The values of x for which the matrix [[x+a,b,c],[a,x+b,c],[a,b,x+c]] is non-singular are (A) R-{0} (B) R-{-(a+b+c)} (C) R-{0,-(a+b+c)} (D) none of these

If |[p, b, c],[ a, q, c],[ a, b, r]|=0, find the value of p/(p-a)+q/(q-b)+r/(r-c),p!=a ,q!=b ,r!=c dot

If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)] , prove that P Q=[(x a,0 ,0 ),(0,y b,0),( 0 ,0,z c)]=Q P

a!=p , b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 the value of p/(p-a)+q/(q-b)+r/(r-c)=