Express w as a linear combination of the vector V1 and V2 if this is possible. If not, Show that it is impossible. w= [3]
[-1]
[2]

v1= [-3]
[1]
[2]

v2= [6]
[-2]
[3]

Step-by-step explanation:

We have the following vectors :

In order to express as a linear combination of the vectors and , we will search for ∈ IR such that :

     (I)

Now we are going to work matrixically with the equation (I) :

Distributing mathematically and matching ''component to component'' we lead to the following equations :

Working with the system associated matrix :

Applying matrix operations we lead to the following equivalent matrix :

In this matrix we obtain that :

 and

We can verify this solution by replacing the values of and in the equation (I) :

 ⇒

   ⇒