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)...+det(M_2007)` `(A) 2007 (B) 2008 (C) (2008)^(2) (D) (2007)^(2)`

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to(a) det (A) (B) 1/(det(A) (C) 1 (D) 0

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to (A) det (A) (B) 1/(det(A) (C) 1 (D) 0

If A is an invertble matrix of order 2 then (det A ^-1) is equal to- a.det A b.1/ det A c. 1 d. 0

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.

If sum _( r -1) ^(n) T_(r) = (n (n +1)(n+2))/(3), then lim _(x to oo) sum _(r =1) ^(n) (2008)/(T_(r))=

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

Let a= 1/(n!) + sum_(r=1)^(n-1) r/((r+1)!), b= 1/(m!)+sum_(r=1)^(m-1) r/((r+1)!)then a+b= (A) 0 (B) 1 (C) 2 (D) none of these

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

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