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<h1 id="function-usolveall">Function usolveAll <a href="#function-usolveall" title="Permalink">#</a></h1>

Finds all solutions of a linear equation system by backward substitution. Matrix must be an upper triangular matrix.

`U * x = b`


<h2 id="syntax">Syntax <a href="#syntax" title="Permalink">#</a></h2>

```js
math.usolveAll(U, b)
```

<h3 id="parameters">Parameters <a href="#parameters" title="Permalink">#</a></h3>

Parameter | Type | Description
--------- | ---- | -----------
`U` | Matrix, Array | A N x N matrix or array (U)
`b` | Matrix, Array | A column vector with the b values

<h3 id="returns">Returns <a href="#returns" title="Permalink">#</a></h3>

Type | Description
---- | -----------
DenseMatrix[] &#124; Array[] | An array of affine-independent column vectors (x) that solve the linear system


<h3 id="throws">Throws <a href="#throws" title="Permalink">#</a></h3>

Type | Description
---- | -----------


<h2 id="examples">Examples <a href="#examples" title="Permalink">#</a></h2>

```js
const a = [[-2, 3], [2, 1]]
const b = [11, 9]
const x = usolveAll(a, b)  // [ [[8], [9]] ]
```


<h2 id="see-also">See also <a href="#see-also" title="Permalink">#</a></h2>

[usolve](usolve.html),
[lup](lup.html),
[slu](slu.html),
[usolve](usolve.html),
[lusolve](lusolve.html)