### Home > PC > Chapter 12 > Lesson 12.2.2 > Problem 12-55

12-55.

Let

Show that

if. Find two other vectors

*b*and*c*such thatand. Think before rushing to compute.In general,

Set up a system of equations and solve for

in terms of.Find a vector

*d*such that.For parts (c), (d), and (e), follow the steps in part (b).

Show that there is no vector

such that.Show that there is no vector

such thatif.Solving for

in the top equation andin the bottom equation:By substitution:

Since we have assumed

, divide byand solve for.