Let `A` be the set of all `3xx3` skew-symmetri matrices whose entries are either `-1,0,or1.` If there are exactly three 0s three 1s, and there `(-1)' s` , then the number of such matrices is __________.

Let A be the set of all 3 xx 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices in A is

Let A be the set of all 3xx3 symmetric matrices all of whose either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices A in A for which the system of linear equations A[(x),(y),(z)]=[(1),(0),(0)] is inconsistent is : (A) less than 4 (B) at least 4 but less than 7 (C) at least 7 but less than 10 (D) at least 10

If S={0,1,4,5,7}then the number of subsets of S is

Let A=[a_("ij")] be a matrix of order 2 where a_("ij") in {-1, 0, 1} and adj. A=-A . If det. (A)=-1 , then the number of such matrices is ______ .

Find the number of all possible matrices of order 3xx3 with each entry 0 or 1. How many of these are symmetric ?

The number of all possible matrices of order 3xx3 with each entry 0 or 1 is :

Let omega != 1 be cube root of unity and S be the set of all non-singular matrices of the form [(1,a,b),(omega,1,c),(omega^2,omega,1)], where each of a,b, and c is either omega or omega^2. Then the number of distinct matrices in the set S is (a) 2 (b) 6 (c) 4 (d) 8

If the entries in a 3xx3 determinant are either 0 or 1, then the greatest value of their determinants is

The number of 3xx3 matrices A whose entries are either 0or1 and for which the system A|[x], [y ],[z]|=|[1], [0],[0]| has exactly two distinct solution is a. 0 b. 2^9-1 c. 168 d. 2

Let T & U be the set of all orthogonal matrices of order 3 over R & the set of all non-singular matrices of order 3 over R respectively. Let A = {-1, 0, 1}, then