From Equations to Matrices

Linear Algebra (Matrices) · Axiom Academy

A system of equations and a grid of numbers are the same thing wearing two outfits. Watch one become the other — then drive it yourself. A whole system, boiled down to its numbers Here is a system of three linear equations — three conditions that must all hold at once. Written out, it is mostly scaffolding : the same variables x, y, z, the same plus signs, the same equals sign, over and over. What actually changes from equation to equation is the numbers . So strip the rest away and only the numbers remain — laid out in a grid. That grid is a matrix. Play the animation: the equations slide together, the coefficients drop into aligned columns, the constants slip past a vertical bar, and the system collapses into its augmented matrix [A | b]. The augmented matrix is the same system with the scaffolding removed — every number kept, in the exact same place. Peel the scaffolding away yourself Drag the handle from full equations toward bare matrix . As you go, the parts that repeat every row fade out in order — first the variables x, y, z, then the + signs, then the = and the bar that splits the constants off. What is left is exactly the augmented matrix [A | b]. Same information start to finish — you only removed the parts that never changed. The equations and the matrix are two views of one object. Edit a number — both views move together

This is the written version of the interactive lesson above. See the full Linear Algebra (Matrices) course.