Exercise · ZW-VECTOR-SPACE-003 · ★☆☆ Basic
If \(v=(2,-3,1)\) in \(\mathbb{R}^3\), what is its additive inverse \(-v\)?
Choose one option.
Show answer
- D. \((-2,3,-1)\)
Explanation
The additive inverse satisfies \(v+(-v)=0\), so every component changes sign: \((-2,3,-1)\).
Review the concept: Vector space
A real vector space is a set \(V\) with an addition and a scalar multiplication by reals satisfying eight axioms; its elements are called vectors, whether arrows, matrices or functions.
\[u+v\in V,\quad cv\in V,\quad (c+d)v=cv+dv\]
More practice problems: vector space
- ZW-VECTOR-SPACE-001 With the usual addition and scalar multiplication, which of these sets is a vector space over ℝ?
- ZW-VECTOR-SPACE-002 In the space of 2× 2 matrices, which is the zero vector?
- ZW-VECTOR-SPACE-004 If v=(4,-7), what is 0· v?
- ZW-VECTOR-SPACE-005 In ℝ^2 we use the usual addition and the product codot(x,y)=(cx, y). Which property fails?
- ZW-VECTOR-SPACE-006 Let S=\f:ℝ→ℝ| f(0)=1\. If f,g∈ S, what is (f+g)(0) and what does it imply?
- ZW-VECTOR-SPACE-007 With the usual operations of ℝ^2, which of these subsets is a vector space?
- ZW-VECTOR-SPACE-008 In any vector space V, what does (-1)· v equal?
- ZW-VECTOR-SPACE-009 On ℝ_>0 define uoplus v=uv and codot u=u^c. What is the zero vector?