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Another way to approach the linear combination is to look at it geometrically. This is where the idea of barycentric coordinates can help. A barycentric coordinate system describes the location of a point as the weighted sum of the regular coordinates of the vertices forming a simplex. In other words, it describes a linear combination with respect to a set of points, where in -dimensional space.
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The solution is building your own tracking system using no-code automation tools. This approach requires more initial setup but provides ongoing monitoring at a fraction of commercial tool costs. The system I built uses Make.com, a no-code automation platform, to query AI models systematically, analyze responses, and track mentions over time. Make offers 1,000 operations monthly on their free tier, making it possible to start tracking without any monetary investment.
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