Question

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
A. less then 4
B. atleast 4 but les then 7
C. atleast 7 but less then 10
D. atleast 10

Answer 1

Correct Answer - B
`[[0,a,b],[a,0,c],[b,c,1]] " either " b=0 or c= 0 rArr abs(A) ne 0 `
`rArr 2` matrices
`[[0,a,b],[a,1,c],[b,c,0]] " either " a=0 or c= 0 rArr abs(A) ne 0 `
`rArr 2` matrices
`[[1,a,b],[a,0,c],[b,c,0]] " either " a=0 or b= 0 rArr abs(A) ne 0 `
`rArr 2` matrices
`[[1,a,b],[a,1,c],[b,c,1]] ` ltbtgt If`a=b=0rArr abs(A) = 0 `
If `a=c=0rArr abs(A) = 0`
If` b= c=0rArr abs(A)=`
`rArr` There will be only 6 matrices.