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Let A be the set of all 3xx3 symmetric m...

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

0

B

more then 2

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
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
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