**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 \(\vec{e}_3\)
**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 \(\vec{e}_3\)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 66E
Related questions
Question
![**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 \(\vec{e}_3\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe5771d5-db1d-47ec-b628-ad0eb0d7f447%2Fe112fa8b-4df1-43c1-801d-98dd3b66d317%2Fkw18z4_processed.png&w=3840&q=75)
Transcribed Image Text:**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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