Linear Algebra problem Please help Somewhat difficult 6 Cons

Linear Algebra problem. Please help. Somewhat difficult

6. Consider a collirtion of linearlv lent veetors tv1. v2. val with v e R3. Is there a free variable in the equation What can you sav about the reduced echelon form of v2 v3 (Hint: Is there a free variable in vi v2 valar 0?)

Solution

For vectors to be linearly independent.

We have two conditions.

1. x₁+x₂+x₃ = 0

2. x1 = x2 = x3 = 0

As it is given that the set of vectors are linearly independent.

All the values of the x is zero.

Hence it does not have any free variables.

The reduced echelon form given the basis of the vectors.corresponding to the reduced echelon form.