Compute the area of the parallelogram determined by u, v,

Chapter 3, Problem 41E

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QUESTION:

Let \(\mathbf{u}=\left[\begin{array}{l}3 \\ 0\end{array}\right]\) and \(\mathbf{v}=\left[\begin{array}{l}1 \\ 2\end{array}\right]\). Compute the area of the parallelogram determined by u, v, u + v, and 0, and compute the determinant of [ u v ]. How do they compare? Replace the first entry of v by an arbitrary number x, and repeat the problem. Draw a picture and explain what you find.

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QUESTION:

Let \(\mathbf{u}=\left[\begin{array}{l}3 \\ 0\end{array}\right]\) and \(\mathbf{v}=\left[\begin{array}{l}1 \\ 2\end{array}\right]\). Compute the area of the parallelogram determined by u, v, u + v, and 0, and compute the determinant of [ u v ]. How do they compare? Replace the first entry of v by an arbitrary number x, and repeat the problem. Draw a picture and explain what you find.

ANSWER:

Solution 41E Picture 4 The determinant of the Matrix whose col

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