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--- math121b:ex3 [2020/02/20 14:36]
pzhou
+++ math121b:ex3 [2020/02/20 15:02] (current)
pzhou
@@ Line 62: / Line 62: @@
  $\begin{pmatrix} 1 & 1  \end{pmatrix} \begin{pmatrix} 3 & 1 \cr 1 & 2 \end{pmatrix} \begin{pmatrix} 1 \cr 1 \end{pmatrix} = 7$
   *  $\| e_1 - 2 e_2 \|^2 =  \begin{pmatrix} 1 & -2  \end{pmatrix} \begin{pmatrix} 3 & 1 \cr 1 & 2 \end{pmatrix} \begin{pmatrix} 1 \cr -2 \end{pmatrix} = 7$
-  * $P(e_1, e_2) = \sqrt{\det(g)} = \sqrt{4} = 2$
+  * $P(e_1, e_2) = \sqrt{\det(g)} = \sqrt{5}$
   * Can you find two vectors  $v_1, v_2 \in \R^2$ , such that  $v_1, v_2$  has the same properties as  $e_1, e_2$ ?  $v_1 = (\sqrt{3}, 0), v_2 = (\sqrt{2} \cos\theta, \sqrt{2} \sin \theta)$  where  $\cos\theta = \frac{1}{\sqrt{2} \sqrt{3}}$ . We are using the formula
  $v \cdot w = \| v \| \|w \| \cos \theta$

Lecture Notes