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

Options

A. 0
B. more then 2
C. 2
D. 1

Answer

B

Explanation

The six matrix A for which `abs(A)= 0` are
`[[0,0,1],[0,0,1],[1,1,1]] rArr` inconsistent
`[[0,1,0],[1,1,1],[0,1,0]] rArr` inconsistent
`[[1,1,0],[1,0,0],[1,0,0]] rArr` infinite solutions
`[[1,1,0],[1,1,0],[0,0,1]] rArr` inconsistent
`[[1,0,1],[0,1,0],[1,0,1]] rArr` inconsistent
`[[1,0,0],[0,1,0],[0,1,1]] rArr` infinite solutions