Prove that (1,1,,1,3) and (5,3,3)form a linearly dependent set.

View Explanation

Concept:

Linear independent is when you set all your vector equal to zero, and the scaling value for each vector is 0. For example:

c₁v₁ + c₂v₂ + c₃v₃ = 0

c₁, c₂, c₃ are arbitrary scaling value for my vectors vₙ. If they are all 0's then it is linearly independent.

0v₁ + 0v₂ + 0v₃ = 0

Linearly dependent is when at least one of the scaling value cₙ is NOT equal to 0.

for example:

c₁v₁ + c₂v₂ + c₃v₃ = 0

0v₁ + 2v₂ + 0v₃ = 0

Here you can see that  c₂ = 2, which is not 0, therefore it is Linearly Dependent.

Step-by-step explanation:

In our problem we are given 3 vectors. I set up the equation

c₁v₁ + c₂v₂ + c₃v₃ = 0

and solve for cₙ using matrice. I row reduced it using matlab because I'm lazy. The result showed that c₁, c₂, c₃≠0, so the answer is linearly dependent.