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Linear Algebra

Solving Ax=b Visually

b is the destination, x is the starting point, and A is the transform between them.

Ax=b asks this

Where should x start so A sends it to b?

This is why inverse and elimination exist. They are not random formulas.

Ax=b setup

A

The left column is where i lands; the right column is where j lands.

b

det(A)3

One solution because undo works

x = (2, 1)

This target undoes to x = (2, 1).

Ax = b

x₁21+x₂12=54

Before A

det = 1

We are looking for x here

A

After A

det = 3

Whole picture:A sends x to bdet says if undo worksinverse/elimination find x

Speed 1.0x

Credits & References