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Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$  be an eigenvector of a $2\times2$ matrix $\text{A}$ with corresponding eigenvalue $\lambda ,\lambda > 0$. If we denote the magnitude of a vector $\text{v}$ by $\left \| v \right \|$, identify the $\text{VALID}$ statement regarding, ${p}'$, where ${p}'=Ap$.

  1. Direction of ${p}'=\lambda \theta ,\left \| {p}' \right \|=\left \| p \right \|$
  2. Direction of ${p}'=\theta ,\left \| {p}' \right \|=\lambda \left \| p \right \|$
  3. Direction of ${p}'=\lambda \theta ,\left \| {p}' \right \|=\lambda \left \| p \right \|$
  4. Direction of ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
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