Given a collection x1, x2, …, xk of vectors in ℝn, we say that the vectors form a linearly...

Given a collection x1, x2, …, xk of vectors in ℝn, we say that the vectors form a linearly dependent set if one of them can be written as a linear combination of the others. That is, the set is linearly dependent if there is an index j in the range 1 to k such that

where the ci’s are given numbers.

Show that the constant k in the last paragraph of Example 2.1.5 is positive if r = 1 and negative if r = −1.