If `A_(i,j)` be the coefficient of `a^i b^j c^(2010-i-j)` in the expansion of `(a+b+c)^2010`, then

Let A = [a_(ij)] be 3 xx 3 matrix given by a_(ij) = {(((i+j)/(2))+(|i-j|)/(2),if i nej,),((i^(j)-(i.j))/(i^(2)+j^(2)),if i n=j,):} where a_(ij) denotes element of i^(th) row and j^(th) column of matrix A. On the basis of above information answer the following question: If a 3 xx3 matrix B is such that A^(2) +B^(2) = A +B^(2)A , then det. (sqrt(2)BA^(-1)) is equal to

Let P=[a_(i j)] be a 3xx3 matrix and let Q=[b_(i j)],w h e r eb_(i j)=2^(i+j)a_(i j) for 1lt=i ,jlt=3. If the determinant of P is 2, then the determinant of the matrix Q is

For a 2xx2 matrix A=[a_(i j)] whose elements are given by a_(i j)=i/j , write the value of a_(12) .

For a\ 2\ xx\ 2\ matrix, A=[a_(i j)], whose elements are given by a_(i j)=i/j , write the value of a_(12)dot

If A=[a_(i j)] is a square matrix of even order such that a_(i j)=i^2-j^2 , then (a) A is a skew-symmetric matrix and |A|=0 (b) A is symmetric matrix and |A| is a square (c) A is symmetric matrix and |A|=0 (d) none of these

If a = i + j, b = j + k and c = i + k then a unit vector in the direction of a - 2b + 3c is

if A=[a_(ij)]_(2*2) where a_(ij)={i+j , i!=j and i^2-2j ,i=j} then A^-1 is equal to

If A=[a_(i j)] is a 2xx2 matrix such that a_(i j)=i+2j , write A .

If a=3i+2j+k, b=5i-j+2k" and "c=i+j+k , find [a b c]

If in a square matrix A=(a_(i j)) we have a_(ji)=a_(i j) for all i , j then A is