My realization

.gitignore

@@ -1,6 +1,101 @@
+<<<<<<< HEAD
+
+# Created by https://www.gitignore.io/api/java,intellij
+# Edit at https://www.gitignore.io/?templates=java,intellij
+
+### Intellij ###
+# Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio and WebStorm
+# Reference: https://intellij-support.jetbrains.com/hc/en-us/articles/206544839
+
+# User-specific stuff
+.idea/**/workspace.xml
+.idea/**/tasks.xml
+.idea/**/usage.statistics.xml
+.idea/**/dictionaries
+.idea/**/shelf
+
+# Generated files
+.idea/**/contentModel.xml
+
+# Sensitive or high-churn files
+.idea/**/dataSources/
+.idea/**/dataSources.ids
+.idea/**/dataSources.local.xml
+.idea/**/sqlDataSources.xml
+.idea/**/dynamic.xml
+.idea/**/uiDesigner.xml
+.idea/**/dbnavigator.xml
+
+# Gradle
+.idea/**/gradle.xml
+.idea/**/libraries
+
+# Gradle and Maven with auto-import
+# When using Gradle or Maven with auto-import, you should exclude module files,
+# since they will be recreated, and may cause churn.  Uncomment if using
+# auto-import.
+# .idea/modules.xml
+# .idea/*.iml
+# .idea/modules
+
+# CMake
+cmake-build-*/
+
+# Mongo Explorer plugin
+.idea/**/mongoSettings.xml
+
+# File-based project format
+*.iws
+
+# IntelliJ
+out/
+
+# mpeltonen/sbt-idea plugin
+.idea_modules/
+
+# JIRA plugin
+atlassian-ide-plugin.xml
+
+# Cursive Clojure plugin
+.idea/replstate.xml
+
+# Crashlytics plugin (for Android Studio and IntelliJ)
+com_crashlytics_export_strings.xml
+crashlytics.properties
+crashlytics-build.properties
+fabric.properties
+
+# Editor-based Rest Client
+.idea/httpRequests
+
+# Android studio 3.1+ serialized cache file
+.idea/caches/build_file_checksums.ser
+
+### Intellij Patch ###
+# Comment Reason: https://github.com/joeblau/gitignore.io/issues/186#issuecomment-215987721
+
+# *.iml
+# modules.xml
+# .idea/misc.xml
+# *.ipr
+
+# IntelliJ IDEA folder
+.idea/
+
+#module
+rujnster.iml
+
+# Sonarlint plugin
+.idea/sonarlint
+
+### Java ###
+# Compiled class file
+*.class
+=======
 # Compiled class file
 *.class
 out/
+>>>>>>> 1bee331b085ecfea6a7af0e9719010f1626939b0
 
 # Log file
 *.log
@@ -23,8 +118,12 @@ out/
 # virtual machine crash logs, see http://www.java.com/en/download/help/error_hotspot.xml
 hs_err_pid*
 
+<<<<<<< HEAD
+# End of https://www.gitignore.io/api/java,intellij
+=======
 # Git
 git.properties
 
 # IntelliJ IDEA folder 
 .idea/
+>>>>>>> 1bee331b085ecfea6a7af0e9719010f1626939b0

in.txt

@@ -0,0 +1,4 @@
+3
+1 1 2 9
+2 4 -3 1
+3 6 -5 0

out.txt

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+1.0 2.0 3.0 

pom.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project xmlns="http://maven.apache.org/POM/4.0.0"
+         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+         xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
+    <modelVersion>4.0.0</modelVersion>
+
+    <groupId>hyperskill</groupId>
+    <artifactId>ru.jnster</artifactId>
+    <version>1.0-SNAPSHOT</version>
+
+    <dependencies>
+        <dependency>
+            <groupId>junit</groupId>
+            <artifactId>junit</artifactId>
+            <version>4.12</version>
+            <scope>test</scope>
+        </dependency>
+    </dependencies>
+
+</project>

src/solver/java/GaussianElimintation/GaussianElimintation.java

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+package GaussianElimintation;
+
+/**
+ * Класс для нахлждения вектора решений системы уравнений методом Гаусса
+ */
+
+public class GaussianElimintation {
+    private Matrix matrix;
+    private double result[];
+    private int N;
+
+    public GaussianElimintation(double[][] matrix) {
+        setMatrix(matrix);
+    }
+
+    public GaussianElimintation(Double[][] matrix) {
+        setMatrix(matrix);
+    }
+
+    public GaussianElimintation(Matrix matrix) {
+        setMatrix(matrix);
+    }
+
+    public double[] findAnswer() {
+        double coefficient;
+        result = new double[N--];
+        for (int counter = 0; counter < N; counter++) {
+            for (int next = counter + 1; next <= N; next++) {
+                coefficient = matrix.getElement(next, counter) / matrix.getElement(counter, counter) * -1;
+                matrix.addRow(coefficient, counter, next, counter);
+            }
+        }
+        for (int counter = N; counter >= 0; counter--) {
+            result[counter] = (matrix.getElement(counter, N + 1) - calculate(counter)) / matrix.getElement(counter, counter);
+        }
+        return result;
+    }
+
+    /**
+     * Проверяет является ли матрица квадратной. Вектор значение после знака равенства не учитывается.
+     *
+     * @param matrix Матрица для проверки, включая столбец значений после знака раменства.
+     * @return true - матрица квадратная, false - нет
+     */
+    public static boolean isSquareMatrix(Matrix matrix) {
+        boolean result = true;
+        int N = matrix.getN();
+        for (Row row : matrix.getRows()) {
+            result &= row.getDoubleList().size() == N + 1;
+        }
+        return result;
+    }
+
+    /**
+     * Вычисление известной части уравнения
+     * @param stage индекс после которого происходит расчёт
+     * @return сумма известных частей полинома
+     */
+    private double calculate(int stage) {
+        double result = 0.0;
+        if (stage != N) {
+            for (int counter = stage + 1; counter <= N; counter++) {
+                result += matrix.getElement(stage, counter) * this.result[counter];
+            }
+        }
+        return result;
+    }
+
+    public void setMatrix(double[][] matrix) {
+        setMatrix(new Matrix(matrix));
+    }
+
+    public void setMatrix(Double[][] matrix) {
+        setMatrix(new Matrix(matrix));
+    }
+
+    public void setMatrix(Matrix matrix) {
+        try {
+            if (!isSquareMatrix(matrix)) throw new RuntimeException("This matrix is not square matrix.");
+        } catch (RuntimeException re) {
+            re.printStackTrace();
+        }
+        this.matrix = matrix;
+        N = this.matrix.getN();
+        result = null;
+    }
+
+    public Matrix getMatrix() {
+        return matrix;
+    }
+
+    public double[] getResult() {
+        if (result == null) result = findAnswer();
+        return result;
+    }
+}

src/solver/java/GaussianElimintation/Main.java

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+package GaussianElimintation;
+
+import java.io.*;
+
+/**
+ * Обязательные аргументы запуска это флаги "-in" и "-out", после которых следует имя файла с исходными данными или
+ * имя файла для вывода значения сооттветственно.
+ */
+
+public class Main {
+    public static void main(String[] args) {
+        BufferedReader in = null;
+        BufferedWriter out = null;
+        double[][] matrix;
+        double[] result;
+        String[] buffer;
+        int N;
+        GaussianElimintation gaussianElimintation;
+
+        try {
+            for (int counter = 0; counter < 4; counter++) {
+                if (args[counter].equals("-in")) {
+                    in = new BufferedReader(new FileReader(args[++counter]));
+                }
+                if (args[counter].equals("-out")) {
+                    out = new BufferedWriter(new FileWriter(args[++counter]));
+                }
+            }
+
+            if (in == null || out == null) return;
+
+            buffer = in.readLine().split(" ");
+            N = Integer.parseInt(buffer[0]);
+            matrix = new double[N][];
+
+            for (int row = 0; row < N; row++) {
+                matrix[row] = new double[N + 1];
+                buffer = in.readLine().split(" ");
+                for (int column = 0; column <= N; column++) {
+                    matrix[row][column] = Double.parseDouble(buffer[column]);
+                }
+            }
+            in.close();
+            gaussianElimintation = new GaussianElimintation(matrix);
+            result = gaussianElimintation.findAnswer();
+            for (int counter = 0; counter < N; counter++) {
+                out.append(Double.toString(result[counter]) + " ");
+            }
+            out.close();
+            System.out.println("Completed!");
+        } catch (IOException e) {
+            e.printStackTrace();
+        }
+    }
+}