Chapter 5.1, Problem 44E

In Exercises 40 through 46, consider vectors ${\stackrel{\to }{v}}_1,{\stackrel{\to }{v}}_2,{\stackrel{\to }{v}}_3$in ${ℝ}^4$; we are told that ${\stackrel{\to }{v}}_i\cdot {\stackrel{\to }{v}}_j$is the entry $a_{ij}$of matrix A.

$A=\left[\begin{array}{ccc}3& 5& 11\\ 5& 9& 20\\ 11& 20& 49\end{array}\right]$

44. Find a nonzero vector $\stackrel{\to }{v}$ in $\text{span}\left({\stackrel{\to }{v}}_2,{\stackrel{\to }{v}}_3\right)$ such that $\stackrel{\to }{v}$ isorthogonal to ${\stackrel{\to }{v}}_3$ . Express ${\stackrel{\to }{v}}_3$ as a linear combination of ${\stackrel{\to }{v}}_2$ and ${\stackrel{\to }{v}}_3$ .