###### Exercise1

Shown in Figure 3.2.11 are two vectors $$\vvec_1$$ and $$\vvec_2$$ in the plane $$\real^2\text{.}$$

1. Explain why $$\bcal=\{\vvec_1,\vvec_2\}$$ is a basis for $$\real^2\text{.}$$

2. Using Figure 3.2.11, indicate the vectors $$\xvec$$ such that

1. $$\coords{\xvec}{\bcal} = \twovec{2}{-1}$$

2. $$\coords{\xvec}{\bcal} = \twovec{-1}{-2}$$

3. $$\coords{\xvec}{\bcal} = \twovec{0}{3}$$

3. Using Figure 3.2.11, find the representation $$\coords{\xvec}{\bcal}$$ if

1. $$\xvec = \twovec{-2}{-1}\text{.}$$

2. $$\xvec = \twovec{2}{4}\text{.}$$

3. $$\xvec = \twovec{2}{-5}\text{.}$$

4. Find $$\coords{\xvec}{\bcal}$$ if $$\xvec=\twovec{60}{90}\text{.}$$

in-context