Is this vector in the range of the matrix transformation?

[mathstresser]

Let f: R^2 --> R^3 be the matrix transformation defined by f(x) = Ax, where

. . .\(\displaystyle \L A\, =\, \left[\, \begin{array}{rr}1&3\\-1&2\end{array}\, \right]\)

Determine whether the given vector w is in the range of f:

. . .\(\displaystyle \L w\, =\, \left[\, \begin{array}{c}7\\3 \end{array}\, \right]\)
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Edited by stapel -- Reason for edit: formatting matrices.

 

[pka]

I think that you want \(\displaystyle f:R^2 \mapsto R^2 .\)

If so, then does the system have a solution?

\(\displaystyle \begin{array}{rcl}
x + 3y & = & 7 \\
- x + 2y & = & 3 \\
\end{array}\)

 

[mathstresser]

x is 1 and y is 2

so then it is in that range...

Thanks ( I didn't know that's all you had to do)