Math Problem Statement
これが一次独立ということを示してください。
Solution
To show that the vectors , , and are linearly independent, we need to verify that the only solution to the equation
is , , and .
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First, expand the given equation:
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Combine like terms:
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For the above polynomial to be identically zero, the coefficients of each power of must be zero. This gives us the following system of equations:
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Vector Spaces
Linear Independence
Formulas
a(x + 1) + b(x^2 - 1) + c(x^3 + 1) = 0
Theorems
Criteria for Linear Independence
Suitable Grade Level
Grades 10-12
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