If `P={:[(a,b),(c,d)]:}andQ={:[(w,x),(y,z)]:}`, then show that `(PQ)^(T)=Q^(T)P^(T)`.

If A={:[(a,p),(b,q),(c,r)]:} , then (A^(T))^(T) = _________ .

If a,b,c,d are in A.P.and x,y,z are in G.P. then show that x^(b-c)*y^(c-a)*z^(a-b)=1

If A=[(a,b,c),(x,y,z),(p,q,r)] and B=[(q,-b,y),(-p,a,-x),(r,-c,z)] then (A) |A|=|B| (B) |A|=-|B| (C) |A|=2|B| (D) none of these

If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)| , then

(2) If a=x^(q+r)*y^(p) , b=x^(r+p)*y^(q) , c=x^(p+q)y^(r) , show that a^(q-r)b^(r-p)c^(p-q)=1

If A=((1,2),(0,1)),P=((costheta, sintheta),(-sintheta, costheta)),Q=P^(T)AP , find PQ^(2014)P^(T) :

If x = a sin 2t(1 + cos 2t) and y = b cos 2 t(1 – cos 2 t), show that ((d y)/(d x))_(at t =pi/4)=b/a.

Consider the following relations from A to B where A={u, v, w, x, y, z} and B={p, q, r, s}. 1. {(u,p),(v,p),(w,p),(x,q),(y,q),(z,q)} 2. {(u,p),(v,q),(w,r),(z,s)} 3. {(u,s),(v,r),(w,q),(u,p),(v,p),(z,q)} 4. {(u,q),(v,p),(w,s),(x,r),(y,q),(z,s)} Which of the above relations are not functions ?