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) = _________ .

For an A.P., show that T_p+T_(p+2q)=2T_(p+q) .

The parametric equations of a curve are given by x-sec^(2)t, y=cot t .If the tangent at P(t=(pi)/(4)) meets the curve again at Q, then show that, PQ=(3sqrt(5))/(2) .

If A=((1,2),(0,1)),P=((costheta, sintheta),(-sintheta, costheta)),Q=P^(T)AP , find PQ^(2014)P^(T) : (a) ((1,2^(2014)),(0,1)) (b) ((1,4028),(0,1)) (c) (P^(T))^(2013)A^(2014)P^(2013) (d) P^(T)A^(2014)P

If p^(t h),\ q^(t h),\ a n d\ r^(t h) terms of an A.P. and G.P. are both a ,\ b\ a n d\ c respectively show that a^(b-c)b^(c-a)c^(a-b)=1.

If the p^(t h) ,q^(t h) and r^(t h) terms of a GP are a, b and c, respectively. Prove that a^(q-r)""b^(r-p)""c^(p-q)=1 .

If the p^(t h) , q^(t h) and r^(t h) terms of a GP are a, b and c, respectively. Prove that a^(q-r)b^(r-p)c^(p-q)=1 .

If the p^(t h) , q^(t h) and r^(t h) terms of a GP are a, b and c, respectively. Prove that a^(q-r)""b^(r-p)""c^(p-q)=1 .