Matrix M_(r) is defined as `M_(r)`= \begin{bmatrix}r & r-1\\r-1 & r\end{bmatrix} `r in N`; Value of `det(M_(1))+det(M_(2))+det(M_(3))+......`

If r,r_(1) ,r_(2), r_(3) have their usual meanings , the value of 1/(r_(1))+1/(r_(2))+1/(r_(3)) , is

Consider two solid sphere of radii R_(1)=1m, R_(2)=2m and masses M_(1) and M_(2) , respectively. The gravitational field due to sphere 1 and 2 are shown. The value of (M_(1))/(M_2)) is:

If M is a 3 xx 3 matrix, where det M=1 and MM^T=1, where I is an identity matrix, prove theat det (M-I)=0.

Assertion: Determinant of a skew symmetric matrix of order 3 is zero. Reason: For any matix A, det(A^T)=det(A) and det(-S)=-det(S) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true and R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

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

Let for A=[(1,0,0),(2,1,0),(3,2,1)] , there be three row matrices R_(1), R_(2) and R_(3) , satifying the relations, R_(1)A=[(1,0,0)], R_(2)A=[(2,3,0)] and R_(3)A=[(2,3,1)] . If B is square matrix of order 3 with rows R_(1), R_(2) and R_(3) in order, then The value of det. (2A^(100) B^(3)-A^(99) B^(4)) is

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)

The figure represents two concentric shells of radii R_(1) and R_(2) and masses M_(1) and M_(2) respectively. The gravitational field intensity at the point A at distance a (R_(1) lt a lt R_(2)) is

If A=[a_(ij)]_(mxxn) is a matrix of rank r then (A) rltmin{m,n} (B) rlemin{m,n} (C) r=min{m,n} (D) none of these

If A=[a_(ij)]_(mxxn) is a matrix of rank r then (A) r=min{m,n} (B) rlemin{m,n} (C) rltmin{m,n} (D) none of these