Calculate a linear combination by scaling each vector with its coefficient and adding the results coordinate by coordinate.
Last updated: June 2026 | By Patchworkr Team
A linear combination is the sum of one or more vectors after each vector has been multiplied by a coefficient. In compact form, v = c1v1 + c2v2 + ... + cnvn.
For c1 = 4, v1 = [2, 1], c2 = 2, and v2 = [-1, 3], the result is [6, 10].
What if a coefficient is blank?
Blank coefficients are rejected so the calculator does not guess a value for you.
Do all vectors need the same dimension?
Yes. Every vector must have the same number of coordinates for the sum to be valid.
Can I add more vectors?
Yes. Use Add Vector to extend the combination with another coefficient and vector.
Does the tool accept decimals?
Yes. Any finite real coefficient or coordinate is accepted, including scientific notation.
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