Algebra Calculators

Algebra homework tends to stall in the same places: an equation that will not rearrange, a matrix that will not resolve, or a log expression that looks different from the answer in the back of the book. The tools here work through those steps directly, showing the result for the values entered rather than explaining the topic in the abstract.

The null space of a matrix is the set of all vectors that the matrix sends to zero, and a basis for it is the compact list of vectors that generates the whole set.

Evaluating a linear function means one small job done carefully: take f(x) = mx + b, replace x with a number, and simplify.

Every straight line crosses the two axes in at most two places, and those two points are enough to sketch the whole line.

An eigenbasis is a basis built entirely from eigenvectors: enough independent eigenvectors to span the whole space, which is exactly the condition for a matrix to be diagonalizable.

Most eigenvalue tools stop at the eigenvalues and leave the vectors, the one part you usually need, as an exercise.

Some matrices stretch space; others twist it.

An eigenspace basis is the short list of vectors that generates every eigenvector belonging to one eigenvalue.

Antidifferentiation is differentiation run in reverse: you are handed a rate, a slope, or a growth rule, and you need the function it came from.

When one whole number does not divide evenly into another, the leftover is the remainder, and it turns up everywhere: packing boxes, splitting bills, scheduling shifts.

The slope between two points is rise over run: how far y climbs for each step in x.