## Solve a System of Equations

## Usage

    solve(a, b, tol = 1e-7)

## Arguments

`a` | a numeric matrix containing the coefficients of the linear system.
`b` | a numeric vector or matrix giving the right-hand side(s) of the linear system. If omitted, `b` is taken to be an identity matrix and `solve` will return the inverse of `a`.
`tol` | the tolerance for detecting linear dependencies in the columns of `a`.

## Description

This generic function solves the equation `a %*% x = b` for `x`, where `b` can be either a vector or a matrix.

## See Also

`backsolve`, `qr.solve`.

## Examples

    hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
    h8 <- hilbert(8); h8
    solve(h8) # gives error: `singular'
    sh8 <- solve(h8, tol = 1e-10)
    round(sh8 %*% h8, 3)

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