Pre-Columbian South American Cultures were excellent accountants and mathematicians. Spanish explorers described how they could calculate with extreme precision the volume of a distant mountain, the size for a water pipe to induce laminar or turbulent flow, or forecast the yield of numerous acres of fields… through the movement of colorful beads around a Yupana (Inca Abacus) and recording of information on Quipus (form of string data in knots: color, knot type and relative location all carrying different meanings)
This description implies the performance of third order differential equations without calculus. Their textiles and ceramics frequently feature diagonally symmetric “Matrices” ONE in particular being called the Inca Key… bearing a strong resemblance to the identity Matrix
So I ask, were they performing linear algebra? And if yes, I challenge you figure out how you could use their Yupana to perform such calculations yourself.