Let A= <br />
\begin{bmatrix}<br />
 a1&a2&a3 \\<br />
  \ b1&b2&b3 \\ <br />
  \ c1&c2&c3\\<br />
\end{bmatrix}<br />
 B=<br />
\begin{bmatrix}<br />
 a1   & a2 \\<br />
  \ b1 & b2 \\ <br />
  \ c1&c2\\<br />
\end{bmatrix}

Suppose B is nonsingular. Bz= <br />
\begin{bmatrix}<br />
  a3   \\<br />
  \ b3 \\ <br />
\end{bmatrix}

Let x be a 3-vector. Show that

 \begin{bmatrix}<br />
a1   & a2 & a3 \\<br />
  \ b1 & b2 & b3 \\ <br />
\end{bmatrix}\ <br />
 x
=
  \begin{bmatrix}<br />
0\\<br />
  \ 0 \\ <br />
\end{bmatrix}
if and only if there is a scalar  \lambda such that
 x= <br />
\lambda<br />
\begin{bmatrix}<br />
z1\\<br />
  \ z2 \\<br />
-1\\ <br />
\end{bmatrix}

b)Show that A is singular if and only if c1z1 + c2z2 = c3

Please somebody help.