Visualize vectors, solve algebra & calculus step by step, with guides
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.
Type a function and see the answer and the reasoning: which rule applies, what each piece becomes, and how the pieces combine. The computation is done by the Nerdamer symbolic library; VectorLab explains it.
Series and more are planned for later.
Find the value f(x) approaches as x gets close to a point or grows without bound. Check from both sides, or from one side only.
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x^2. Products: 3x or 3*x.sin cos tan sec ln log exp sqrt abs; constants pi and e.inf or -inf. Left and right limits are only used for finite points.Enter a function and the value x approaches, or choose an example. You will get the answer, the reasoning, and a graph around that point.
Answer
Differentiate a function up to four times. The rule is named, each piece is worked out, and f and its derivative are plotted together.
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x^2. Products: 3x or 3*x.sin cos tan sec ln log exp sqrt abs; constants pi and e.Enter a function of x and choose the order, or pick an example to see the working.
Answer
Find an antiderivative F(x) of f(x), with the rule named at each step. The constant C is added for you.
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x^2. Products: 3x or 3*x.sin cos tan sec ln log exp sqrt abs; constants pi and e.x.Enter a function of x, or pick an example. The answer comes first, followed by the full working.
Answer
Evaluate the integral of f(x) between two bounds: the antiderivative, both substitutions, and the exact and decimal answer.
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x^2. Products: 3x or 3*x.sin cos tan sec ln log exp sqrt abs; constants pi and e.pi, 1/2, sqrt(2).x.Enter a function and two bounds, or pick an example. You will see the antiderivative and both substitutions.
Answer
Concise, beginner-friendly notes on when and why each method is used. Open a guide to read it, or try the method on an example in the calculator.
VectorLab is a free, browser-based tool for learning linear algebra, polynomials and calculus. It shows the working, not just the answer: every row operation, every pivot, every line of a long division, and the rule behind every limit, derivative and integral.
New to a method? Use the Method guide button above the tools, or browse all the written guides with worked examples. Read more about the site.