**Does the ordered set \(\{ \vec{v}_1, \vec{v}_2, \vec{v}_3\} \) form a basis for \(\mathbb{R}^3\)? If not, which vectors would you subtract from the set and which standard basis vector can you add to the set to make it a basis for \(\mathbb{R}^3\)?** \[ \vec{v}_1 = (1, -1, -2) \] \[ \vec{v}_2 = (5, -4, -7) \] \[ \vec{v}_3 = (-3, 1, 0) \] Select all answers that are correct. - [ ] subtract vector \(\vec{v}_1\) from the set - [ ] no it does not form a basis for \(\mathbb{R}^3\) - [ ] subtract vector \(\vec{v}_3\) from the set - [ ] yes it forms a basis for \(\mathbb{R}^3\) - [ ] add vector \(\vec{e}_1\) - [ ] add vector \(\vec{e}_2\) - [ ] subtract vector \(\vec{v}_2\) from the set - [ ] add vector \(\vec{e}_3\)

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