- #1

lonewolf219

- 186

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## Homework Statement

Determine if vectors

<1,-1,0,2,3>

<1,0,-1,3,3>

<1,-1,0,3,0>

<0,1,-1,2,-2>

are linearly dependent or independent

## Homework Equations

I have been solving these questions in the book using a matrix and row reducing them. If I wound up with a free variable, I determined the vectors to be linearly dependent. If there was no free variable after row reducing, then I determined the vectors were linearly independent. From the examples in the book, this method worked (unless just by chance?)

## The Attempt at a Solution

This is the problem that appeared on the first exam. I solved as described, and found a free variable; the answer was marked wrong. I thought the existence of a parameter in a solution set meant that at least two of the vectors were in the same span, therefore linearly dependent. Am I mistaken?