Question

The number of `3xx3` matrices `A` whose entries are either `0or1` and for which the system `A[x y z]=[1 0 0]` has exactly two distinct solution is a. 0 b. `2^9-1` c. `168` d. `2`

Answer 1

Correct Answer - A
Let `A=[(x),(y),(z)]=[(1),(0),(0)]`
`impliesax+by+cz=1,px+qy+rz=0,lx+my+nz=0`
This gives three planes which cannot intersect at two distinct ponts. So there cannot be any `3xx3` matrix for which the given system of equations has two distinct solutions.