Online Algebra Calculator

Many of users do not use powerful **Maxima computer algebra system** for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only.
To do this job, it is not useful to download the whole application from a web site.

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Null Space (also Kernel matrix) is the set of all vectors `v`

of matrix `M`

for which `Mv=0`

.

Given matrix:

in maxima:

`m:matrix([1,1,-1],[1,5,1],[1,-1,-2]);`

The null space of this matrix consists of all vectors `(x, y, z) ∈ R`

for which:^{3}

This can be written as a system of linear equations:

in maxima:

```
eq1:x+y-z=0;
eq2:x+5*y+z=0;
eq3:x-y-2*z=0;
```

We can solve these equations

in maxima:

`linsolve([eq1,eq2,eq3],[x,y,z]);`

We can write the null space (solution to `Mv = 0`

) in terms of `c`

, where `c`

is scalar

Since `c`

is a free variable this can be simplified for example to

`n:matrix([3/2],[-(1/2)],[1]);`

`m.n`