If `A=[[(1,1)],[(1,1)]]` and `n inN`, then `A^n=2^(n-1)A` .

If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}],k epsilon N

If P(n-1,3):P(n+1,3)=5:12 , find n.

If P(n-1,3):P(n+1,3)=5:12,"Find "n .

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are the direction cosines of two mutually perpendicular lines show that the Direction Cosines of the line perpendicular to both of them are m_(1)n_(2) - n_(1)m_(2), n_(1)l_(2) - l_(1)n_(2), l_(1)m_(2) - m_(1)l_(2)

If 2x=y^(1/m)+y^(-1/m) , then prove that (x^2-1)y_(n+2)+(2n+1)xy_(n+1)+(n^2-m^2)y_n=0 .

x^n - y^n = (x-y) (x^(n-1) + x^(n-2) y + … + xy^(n-2) + y^(n-1)) , x,y in R

Show that the curves y = 2^(x) and y = 5^(x) intersect at an angle tan^(-1) |("1n ((5)/(2)))/(1 + 1n 2 1n 5)| . Note Angle between two curves is the angle between their tangents at the point of intersection.