detials =Mk°, 10 elan. 1.1 ¦••••¦. 11[1=Mk°, 10 elan. 1.1 ¦••••¦. 11[1

(a) 0 rank is impossible, as there are nonzero entries in the matrix.
(b) 1 rank is impossible, since there are odd number of 1 entries in the matrix, any number of row
operations we do, they do not cancel each other.
(c) [



]
(d) [



]

Let us prove that
( )
and
( )
have the same solutions. It follows easily that
( ) ( )
It is clear that solutions of (2) are solutions of (1).
Now suppose x is a solution of (1).
Then multiply (1) by to the left,
( ) ( )
We assume here that A is a real matrix and x is a real vector, hence we get Ax = 0.
This implies that the solutions of (1) are the solutions of (2).
Note...