The number of `3xx3` matrices A whose are ether 0 or 1
and for which the system `A [[x],[y],[z]]=[[1],[0],[0]]` has exactly two
distinct solutions, is

Options

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

Answer

B

Explanation

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