diff --git a/back-end/composer.lock b/back-end/composer.lock
index 87f2d80..6fd66b9 100644
--- a/back-end/composer.lock
+++ b/back-end/composer.lock
@@ -35,6 +35,7 @@
             ],
             "description": "Promoting the interoperability of container objects (DIC, SL, etc.)",
             "homepage": "https://github.com/container-interop/container-interop",
+            "abandoned": "psr/container",
             "time": "2017-02-14T19:40:03+00:00"
         },
         {
@@ -173,6 +174,75 @@
             ],
             "time": "2018-10-13T23:28:42+00:00"
         },
+        {
+            "name": "markbaker/matrix",
+            "version": "1.2.0",
+            "source": {
+                "type": "git",
+                "url": "https://github.com/MarkBaker/PHPMatrix.git",
+                "reference": "5348c5a67e3b75cd209d70103f916a93b1f1ed21"
+            },
+            "dist": {
+                "type": "zip",
+                "url": "https://api.github.com/repos/MarkBaker/PHPMatrix/zipball/5348c5a67e3b75cd209d70103f916a93b1f1ed21",
+                "reference": "5348c5a67e3b75cd209d70103f916a93b1f1ed21",
+                "shasum": ""
+            },
+            "require": {
+                "php": "^5.6.0|^7.0.0"
+            },
+            "require-dev": {
+                "dealerdirect/phpcodesniffer-composer-installer": "dev-master",
+                "phpcompatibility/php-compatibility": "dev-master",
+                "phploc/phploc": "^4",
+                "phpmd/phpmd": "dev-master",
+                "phpunit/phpunit": "^5.7",
+                "sebastian/phpcpd": "^3.0",
+                "squizlabs/php_codesniffer": "^3.0@dev"
+            },
+            "type": "library",
+            "autoload": {
+                "psr-4": {
+                    "Matrix\\": "classes/src/"
+                },
+                "files": [
+                    "classes/src/functions/adjoint.php",
+                    "classes/src/functions/antidiagonal.php",
+                    "classes/src/functions/cofactors.php",
+                    "classes/src/functions/determinant.php",
+                    "classes/src/functions/diagonal.php",
+                    "classes/src/functions/identity.php",
+                    "classes/src/functions/inverse.php",
+                    "classes/src/functions/minors.php",
+                    "classes/src/functions/trace.php",
+                    "classes/src/functions/transpose.php",
+                    "classes/src/operations/add.php",
+                    "classes/src/operations/directsum.php",
+                    "classes/src/operations/subtract.php",
+                    "classes/src/operations/multiply.php",
+                    "classes/src/operations/divideby.php",
+                    "classes/src/operations/divideinto.php"
+                ]
+            },
+            "notification-url": "https://packagist.org/downloads/",
+            "license": [
+                "MIT"
+            ],
+            "authors": [
+                {
+                    "name": "Mark Baker",
+                    "email": "mark@lange.demon.co.uk"
+                }
+            ],
+            "description": "PHP Class for working with matrices",
+            "homepage": "https://github.com/MarkBaker/PHPMatrix",
+            "keywords": [
+                "mathematics",
+                "matrix",
+                "vector"
+            ],
+            "time": "2019-10-06T11:29:25+00:00"
+        },
         {
             "name": "monolog/monolog",
             "version": "1.24.0",
@@ -354,21 +424,22 @@
         },
         {
             "name": "phpoffice/phpspreadsheet",
-            "version": "1.5.1",
+            "version": "1.8.0",
             "source": {
                 "type": "git",
                 "url": "https://github.com/PHPOffice/PhpSpreadsheet.git",
-                "reference": "7f46932b2fabbaaf5a70e67cacc472a50b95cbb9"
+                "reference": "0e6238c69e863b58aeece61e48ea032696c6dccd"
             },
             "dist": {
                 "type": "zip",
-                "url": "https://api.github.com/repos/PHPOffice/PhpSpreadsheet/zipball/7f46932b2fabbaaf5a70e67cacc472a50b95cbb9",
-                "reference": "7f46932b2fabbaaf5a70e67cacc472a50b95cbb9",
+                "url": "https://api.github.com/repos/PHPOffice/PhpSpreadsheet/zipball/0e6238c69e863b58aeece61e48ea032696c6dccd",
+                "reference": "0e6238c69e863b58aeece61e48ea032696c6dccd",
                 "shasum": ""
             },
             "require": {
                 "ext-ctype": "*",
                 "ext-dom": "*",
+                "ext-fileinfo": "*",
                 "ext-gd": "*",
                 "ext-iconv": "*",
                 "ext-libxml": "*",
@@ -379,11 +450,13 @@
                 "ext-xmlwriter": "*",
                 "ext-zip": "*",
                 "ext-zlib": "*",
-                "markbaker/complex": "^1.4.1",
+                "markbaker/complex": "^1.4",
+                "markbaker/matrix": "^1.1",
                 "php": "^5.6|^7.0",
                 "psr/simple-cache": "^1.0"
             },
             "require-dev": {
+                "doctrine/instantiator": "^1.0.0",
                 "dompdf/dompdf": "^0.8.0",
                 "friendsofphp/php-cs-fixer": "@stable",
                 "jpgraph/jpgraph": "^4.0",
@@ -441,7 +514,7 @@
                 "xls",
                 "xlsx"
             ],
-            "time": "2018-11-20T19:51:42+00:00"
+            "time": "2019-06-30T22:55:25+00:00"
         },
         {
             "name": "pimple/pimple",
@@ -1836,6 +1909,7 @@
                 "mock",
                 "xunit"
             ],
+            "abandoned": true,
             "time": "2017-06-30T09:13:00+00:00"
         },
         {