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)]`
has a unique solution is

Options

A. less than 4
B. at least 4 but less than 7
C. at least 7 but less than 10
D. at leat 10

Answer

B

Explanation

`[(0,a,b),(a,0,c),(b,c,1)]`
Either `b=0` or `c=0implies |A| ne 0`
`implies` two matrices
`A=[(0,a,b),(a,1,c),(b,c,0)]`
Either `a=0` or `c=0 implies |A| ne 0`
`implies` two matrices
`A=[(1,a,b),(a,0,c),(b,c,0)]`
Either `a=0` or `b=0implies |A| ne 0`
`implies` two matrices
`A=[(1,a,b),(a,1,c),(b,c,1)]`
`a=b=0 implies |A|=0`
`a=c=0 implies |A|=0`
`b=c=0 implies |A| =0`
Therefore, there will be only six matrices.