Math Solutions

[Steps Shown] Let f: R^3 \rightarrow R^3 be a matrix transformation defined by f(x)=A x, where

Question: Let \(f: R^{3} \rightarrow R^{3}\) be a matrix transformation defined by \(f(x)=A x\), where

\[A=\left[\begin{array}{ccc} 2 & 0 & 3 \\ 4 & -1 & 1 \\ 3 & -3 & 2 \end{array}\right]\]

Determine whether each given vector \(w\) is in the range of f:

  1. \(w=\left[\begin{array}{c}-1 \\ 1 \\ -5\end{array}\right]\)
  2. \(w=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]\)
  3. \(w=\left[\begin{array}{c}11 \\ 14 \\ 5\end{array}\right]\)
  4. \(w=\left[\begin{array}{c}10 \\ 7 \\ 4\end{array}\right]\)

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