mathjs/docs/reference/functions/usolveAll.md

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# Function usolveAll

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

`U * x = b`


## Syntax

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

### Parameters

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

### Returns

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


## Examples

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


## See also

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