Exercise 3

Suppose that $$\wvec_1=\fourvec110{-1}, \hspace{24pt} \wvec_2=\fourvec1011$$ form an orthogonal basis for a subspace $W$ of $\real^4$.

1. Find $\bhat$, the orthogonal projection of $\bvec=\fourvec{2}{-1}{-6}{7}$ onto $W$.

2. Find the vector $\bvec^\perp$ in $W^\perp$ such that $\bvec = \bhat + \bvec^\perp$.

3. Find a basis for $W^\perp$. and express $\bvec^\perp$ as a linear combination of the basis vectors.