If `bc +qr=ca+rp=ab+pq=-1`,
show that `|{:(ap,bp,cr),(a,b,c),(p,q,r):}|=0`

Evaluate Delta=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2):}|=4a^2b^2c^2

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0

Using properties of determinants in Exercise 11 to 15 prove that |{:(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c):}|=3(a+b+c)(ab+bc+ca)

If pnea,qneb,rnec and |{:(p,b,c),(a,q,c),(a,b,r):}|=0 then prove that p/(p-a)+q/(q-b)+r/(r-c)=2

Without expanding the determinant prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

If p^(th),q^(th)and r^(th) tern of G.P are a,b and c respectively then |{:(loga,p,1),(logb,q,1),(logc,r,1):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 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 pth,qth and rth terms of an A.P. are a, b, c respectively, then show that a(q-r)+b(r-p)+c(p-q)=0