The sum of the products of elements of any row with the co-factors of corresponding elements is equal to ……..

Let A = [a_(ij)] " be a " 3 xx3 matrix and let A_(1) denote the matrix of the cofactors of elements of matrix A and A_(2) be the matrix of cofactors of elements of matrix A_(1) and so on. If A_(n) denote the matrix of cofactros of elements of matrix A_(n -1) , then |A_(n)| equals

How would you account for the following? The atomic radii of the metals of the third (5d) series of transition elements are virtually the same as those of the corresponding members of the second (4d) series.

Let A be a set of n (>=3) distinct elements. The number of triplets (x, y, z) of the A elements in which at least two coordinates is equal to

If the fourth Power of the common difference of an A.P. with integer entries is added to the product of any four consecutive terms of it, prove that the resulting Sum is the square of an integer.

In a square matrix A of order 3 the elements a_(ii) 's are the sum of the roots of the equation x^(2) - (a+b) x + ab =0, a_(i,i+1) 's are the product of the roots, a_(i,i-1) 's are all unity and the rest of the elements are all zero. The value of the det (A) is equal to

Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8,2, 1/2 .

If Delta= {:|(5,3,8),(2,0,1),(1,2,3)| , write the co-factor of the element a_32

Fill in the Blanks: Area of triangle is _________ the product of any of its sides and corresponding altitude.