Linear algebra visualizer & step-by-step algebra solver
Type numbers or fractions like 1/3. Arrow keys nudge a value by 0.5 (Shift: 0.1).
Drag a vector tip on the plane, or type components. The checkbox includes or excludes a vector from the span.
Type integers, decimals or fractions like 1/3. Arrow keys nudge a value by 0.5 (Shift: 0.1); Enter moves to the next cell.
Drag on the scene to rotate, scroll to zoom. The checkbox includes or excludes a vector from the span.
Columns of A become the transformed vectors Ae₁, Ae₂, Ae₃ below.
Uses matrix A from the Row reduction tab — edit it there to change the null space here.
A₄-column matrix has a null space in ℝ⁴, which can't be drawn — the basis vectors above are its exact mathematical representation.
True forward elimination to row-echelon form: every pivot search, row swap and row operation is shown as its own step, and the system is solved (unique / infinite / no solution) by real back-substitution — not Gauss–Jordan.
Cells accept integers, decimals, negatives, and fractions like -3/4. The last column is the right-hand side of each equation. This performs true Gaussian elimination to row-echelon form (no forced leading 1s, nothing cleared above a pivot) then interprets the result — it does not run Gauss-Jordan.
Pick a method below — each one is its own card, worked through one step at a time.
Type ^ then digits for a power — the exponent gets its own small raised box, same as it will look in the rendered steps below. Works for any divisor.
Synthetic division only works for a monic linear divisor — something like x - 2 or x + 3 (leading coefficient 1). For anything else, use Long division.
Note: the denominator must be entered already factored — e.g. (x-2)(x+1)^2(x^2+1), not the expanded form. This solver decomposes; it does not factor for you.