Linear transformation: find eqn to column vector is in range

[kidia]

Any idea in this one please,Let T:R^3----R^3 be a linear transformation defined by T(X)=AX,where A=
| 1 2 4 |
| 2 3 5 |
|-1-3-7|

Find an equation relating b1,b2 and b3 so that a column vector
|b1|
|b2|
|b3|
will lie in the range of T

 

[pka]

Multiply: \(\displaystyle \L\left[ {\begin{array}{rrr}
1 & 2 & 4 \\
2 & 3 & 5 \\
{ - 1} & { - 3} & { - 7} \\
\end{array}} \right]\left[ {\begin{array}{c}
{b_1 } \\
{b_2 } \\
{b_3 } \\
\end{array}} \right]\)