Task: Gaussian elimination
Go: package main

import (
    "errors"
    "fmt"
    "log"
    "math"
)

type testCase struct {
    a [][]float64
    b []float64
    x []float64
}

var tc = testCase{
    
    
    
    a: [][]float64{
        {1.00, 0.00, 0.00, 0.00, 0.00, 0.00},
        {1.00, 0.63, 0.39, 0.25, 0.16, 0.10},
        {1.00, 1.26, 1.58, 1.98, 2.49, 3.13},
        {1.00, 1.88, 3.55, 6.70, 12.62, 23.80},
        {1.00, 2.51, 6.32, 15.88, 39.90, 100.28},
        {1.00, 3.14, 9.87, 31.01, 97.41, 306.02}},
    b: []float64{-0.01, 0.61, 0.91, 0.99, 0.60, 0.02},
    x: []float64{-0.01, 1.602790394502114, -1.6132030599055613,
        1.2454941213714368, -0.4909897195846576, 0.065760696175232},
}


const ε = 1e-13

func main() {
    x, err := GaussPartial(tc.a, tc.b)
    if err != nil {
        log.Fatal(err)
    }
    fmt.Println(x)
    for i, xi := range x {
        if math.Abs(tc.x[i]-xi) > ε {
            log.Println("out of tolerance")
            log.Fatal("expected", tc.x)
        }
    }
}

func GaussPartial(a0 [][]float64, b0 []float64) ([]float64, error) {
    
    m := len(b0)
    a := make([][]float64, m)
    for i, ai := range a0 {
        row := make([]float64, m+1)
        copy(row, ai)
        row[m] = b0[i]
        a[i] = row
    }
    
    
    for k := range a {
        
        iMax := k
        max := math.Abs(a[k][k])
        for i := k + 1; i < m; i++ {
            if abs := math.Abs(a[i][k]); abs > max {
                iMax = i
                max = abs
            }
        }
        if a[iMax][k] == 0 {
            return nil, errors.New("singular")
        }
        
        a[k], a[iMax] = a[iMax], a[k]
        
        for i := k + 1; i < m; i++ {
            
            for j := k + 1; j <= m; j++ {
                a[i][j] -= a[k][j] * (a[i][k] / a[k][k])
            }
            
            a[i][k] = 0
        }
    }
    
    
    x := make([]float64, m)
    for i := m - 1; i >= 0; i-- {
        x[i] = a[i][m]
        for j := i + 1; j < m; j++ {
            x[i] -= a[i][j] * x[j]
        }
        x[i] /= a[i][i]
    }
    return x, nil
}

PHP: function swap_rows(&$a, &$b, $r1, $r2)
{
    if ($r1 == $r2) return;

    $tmp = $a[$r1];
    $a[$r1] = $a[$r2];
    $a[$r2] = $tmp;

    $tmp = $b[$r1];
    $b[$r1] = $b[$r2];
    $b[$r2] = $tmp;
}

function gauss_eliminate($A, $b, $N)
{
    for ($col = 0; $col < $N; $col++)
    {
        $j = $col;
        $max = $A[$j][$j];

        for ($i = $col + 1; $i < $N; $i++)
        {
            $tmp = abs($A[$i][$col]);
            if ($tmp > $max)
            {
                $j = $i;
                $max = $tmp;
            }
        }

        swap_rows($A, $b, $col, $j);

        for ($i = $col + 1; $i < $N; $i++)
        {
            $tmp = $A[$i][$col] / $A[$col][$col];
            for ($j = $col + 1; $j < $N; $j++)
            {
                $A[$i][$j] -= $tmp * $A[$col][$j];
            }
            $A[$i][$col] = 0;
            $b[$i] -= $tmp * $b[$col];
        }
    }
    $x = array();
    for ($col = $N - 1; $col >= 0; $col--)
    {
        $tmp = $b[$col];
        for ($j = $N - 1; $j > $col; $j--)
        {
            $tmp -= $x[$j] * $A[$col][$j];
        }
        $x[$col] = $tmp / $A[$col][$col];
    }
    return $x;
}

function test_gauss()
{
    $a = array(
        array(1.00, 0.00, 0.00,  0.00,  0.00, 0.00),
        array(1.00, 0.63, 0.39,  0.25,  0.16, 0.10),
        array(1.00, 1.26, 1.58,  1.98,  2.49, 3.13),
        array(1.00, 1.88, 3.55,  6.70, 12.62, 23.80),
        array(1.00, 2.51, 6.32, 15.88, 39.90, 100.28),
        array(1.00, 3.14, 9.87, 31.01, 97.41, 306.02)
    );
    $b = array( -0.01, 0.61, 0.91, 0.99, 0.60, 0.02 );

    $x = gauss_eliminate($a, $b, 6);

    ksort($x);
    print_r($x);
}

test_gauss();