| spanning set |
✓ |
The vectors $(1, 0)$, $(0, 1)$, and $(1, 1)$ form a spanning set of $\reals^2$, because every vector $(x, y)$ is $x (1, 0) + y (0, 1) + 0 (1, 1)$.
|
| pairwise linearly independent |
✓ |
The vectors $(1, 0)$, $(0, 1)$, and $(1, 1)$ are pairwise linearly independent, because no one of the three vectors is a scalar multiple of another.
|
| basis |
✗ |
The vectors $(1, 0)$, $(0, 1)$, and $(1, 1)$ are not a basis of $\reals^2$. They span $\reals^2$, but they are not independent: $(1, 1) = (1, 0) + (0, 1)$, so $(1, 1)$ is redundant.
|
| linearly independent |
✗ |
The vectors $(1, 0)$, $(0, 1)$, and $(1, 1)$ are not linearly independent, because $(1, 1) = (1, 0) + (0, 1)$.
|
| orthogonal |
✗ |
The vectors $(1, 0)$, $(0, 1)$, and $(1, 1)$ are not orthogonal, because the dot product of $(1, 0)$ and $(1, 1)$ is $1$.
|
| orthonormal |
✗ |
The vectors $(1, 0)$, $(0, 1)$, and $(1, 1)$ are not orthonormal, because the vectors are not orthogonal.
|