Matrix `M_(r)` is defined as `M_(r)= [[r, r-1],[ r-1 ,r]], r in N`; Value of `det(M_(1))+det(M_(2))+det(M_(3))+......+det(M_(2007))` is

Matrix M_(r) is defined as M_(r) = ({:(r,r-1),(r-1,r):}), r in N. The value of det (M_(1)) + det (M_(2)) + det (M_(3))+ .... ) det (M_(2014)) is

If A=[(5, -6),(1,-1)] then the value of ("det"(A^(m)-5A^(m-1)))/("det"(A^(n)-5A^(n-1)))(m, "n" in N) is

The value of sum_(r=0)^(3m)(-1)^(r).6mC_(2r) is

The value of sum_(r=1)^(3m)(-3)^(r-1).6mC_(2r-1) is

If A=[{:(2,3),(-1,-2):}] and B=sum_(r=1)^(10)A^r , then the value of det (B)is equal to

If M is the matrix [(1,-3),(-1,1)] then find matrix sum_(r=0)^(oo) ((-1)/3)^(r) M^(r+1)

Two planets of radii R_(1) and R_(2 have masses m_(1) and M_(2) such that (M_(1))/(M_(2))=(1)/(g) . The weight of an object on these planets is w_(1) and w_(2) such that (w_(1))/(w_(2))=(4)/(9) . The ratio R_(1)/R_(2)