Exercise 7.4

Let $x^{(1)},y^{(1)},x^{(2)}$ and $y^{(2)}$ be nonzero vectors in ${ℝ}^3$ with the property that $x^{(1)}$ and $y^{(1)}$ are linearly independent and so are $x^{(2)}$ and $y^{(2)}$. Consider the two planes in

Suppose we wish to find a nonzero vector $v\in {ℝ}^3$ that lies in the intersection $P=P^{(1)}\cap P^{(2)}$. Devise a method for solving this problem by reducing it to the computation of QR factorizations of three $3\times 2$ matrices.