Frequently Asked Questions
How do I check if a vector b is a linear combination of v1, v2?
Form the system c1·v1 + c2·v2 = b. Solve using Gauss-Jordan elimination. If a consistent solution exists, b is a combination; the c values are the coefficients.
Are linear combinations only for 3D vectors?
No. They work in any dimension - including infinite dimensions like function spaces. The math is the same: scale each vector by its coefficient and sum.
What is a unique vs. infinite-many combination?
If the vectors are linearly independent, the combination is unique. If they are dependent, there are infinitely many ways to write the same target.
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