Exercise 4

Consider the vectors $$\wvec_1=\fourvec1100,\hspace{24pt} \wvec_2=\fourvec0011,\hspace{24pt} \bvec=\fourvec2{-4}13.$$

1. If $L$ is the line defined by the vector $\wvec_1$, find the vector in $L$ closest to $\bvec$. Call this vector $\bhat_1$.

2. If $W$ is the subspace spanned by $\wvec_1$ and $\wvec_2$, find the vector in $W$ closest to $\bvec$. Call this vector $\bhat_2$.

3. Determine whether $\bhat_1$ or $\bhat_2$ is closer to $\bvec$ and explain why.