Given the vectors: [4, 3, 3], [0, 1, 1], and [-1, 0, 0]
The question: Is the vector [4, 4, 3] in the span of the set? I believe it is NOT, since putting the augmented matrix for this set in row-reduced echelon form results in an inconsistent set.
Now, I am asked to give a geometric interpretation of the set. I thought it would be a plane (since it can't be a 3D space if the vector is not in the span), but I am unsure about what the answer is and how to reach it. Any help would be greatly appreciated, thank you!
It is not because in any linear combinations of the given vectors the second and third coordinates are always the same. The span is the plane $\{(x,y,z): y=z\}$.