Hi I've been getting ready for my finals and I am not quite sure if I answered the questions right. Can I have your opinions on it please?
Exercise: a-) Is it true that two vectors of R3 are necessarily linearly independent?
b) Is it possible to express the vector u =(1 1 1) as a combination of the vectors v = (1 1 0) and w = ( 1 0 1)?
What I've done a) Two space vectors are linearly independent if and only if the combination of xu+yv = 0 with x=0 and y = 0. The assertion is false.
b/ enter image description here
I concluded that the vector u cannot be expressed by the vectors v and w.
A) the vectors (1,0,0) , (2,0,0) are linearly dependent vectors in R^3. B) Hint: Set up a system of equations.