Math Problem Statement
Solution
The problem states that is the inverse element of the vector in , the real 3-dimensional vector space. To find the value of , we need to determine the inverse of the given vector.
In a vector space, the inverse of a vector is the vector because adding them results in the zero vector .
Thus, the inverse of is . Therefore, we have:
Now, we compute :
Thus, the value of is .
Would you like more details on the concept of inverse elements in vector spaces? Here are some related questions to expand your understanding:
- What is the general formula for finding the inverse of a vector in any vector space?
- How do inverse elements behave under vector addition?
- Can you explain the properties of vector spaces, particularly the identity and inverse elements?
- How is the dot product of vectors related to the inverse of a vector?
- What are some real-world applications of inverse elements in vector spaces?
Tip: In any vector space, the inverse of a vector is simply the negation of each of its components.
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Math Problem Analysis
Mathematical Concepts
Vector Space
Inverse Elements
Vector Addition
Formulas
Inverse of a vector (x, y, z) is (-x, -y, -z)
Theorems
Properties of Vector Spaces
Inverse Elements in Vector Spaces
Suitable Grade Level
Grades 10-12
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