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How did Seki Takakazu’s methods resemble determinants?

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East Asian mathematics Counting boards and markers, or counting rods, were used in China to solve systems of linear equations. This is an example from the 1st century ce.

Seki Takakazu, a foundational figure in the Japanese wasan tradition, developed mathematical procedures that were equivalent to the computation of determinants.12

When working to solve problems involving multiple unknowns, Seki needed a way to eliminate variables between simultaneous equations. To achieve this, he created a "literal" written algebra that replaced the traditional, cumbersome use of counting rods with a system of characters. By expressing coefficients as numbers, parameters, or other unknowns, he established systematic procedures to eliminate variables that functioned in the same manner as modern determinant calculations.132

Historians recognize Seki as the earliest mathematician to use these methods systematically, a development that occurred independently of and contemporaneously with similar work by Gottfried Wilhelm Leibniz in Europe. These advancements allowed Seki and his school to solve complex equations that had previously remained intractable.21