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

Options

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

Answer

B

Explanation

The six matrices A for which `|A|=0` are :
`[(0,0,1),(0,0,1),(1,1,1)]` (inconsistent)
`[(0,1,0),(1,1,1),(0,1,0)]` (inconsistent)
`[(1,1,1),(1,0,0),(1,0,0)]` (infinite solutions)
`[(1,1,0),(1,1,0),(0,0,1)]` (inconsistent)
`[(1,1,0),(1,1,0),(0,0,1)]` (inconsistent)
`[(1,0,1),(0,1,0),(1,0,1)]` (inconsistent)
`[(1,0,0),(0,1,1),(0,1,1)]` (inconsistent)