From cbf4cbbaa903b928fa941d72d55b5949b5f30f71 Mon Sep 17 00:00:00 2001
From: Ravi Ranjan <65977290+RanjanRavi2398@users.noreply.github.com>
Date: Sun, 20 Aug 2023 19:13:41 +0530
Subject: [PATCH 1/2] Update Chapter 1 - Linear Equation System.ipynb

Rewriting the equation , after subtituing their respective value
---
 Chapter 1 - Linear Equation System.ipynb | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Chapter 1 - Linear Equation System.ipynb b/Chapter 1 - Linear Equation System.ipynb
index 784da25..c2f61ed 100644
--- a/Chapter 1 - Linear Equation System.ipynb	
+++ b/Chapter 1 - Linear Equation System.ipynb	
@@ -1046,10 +1046,10 @@
     "We substitute all the points:\n",
     "\n",
     "\\begin{align}\n",
-    "(x,y)&=(1,3)\\qquad\\longrightarrow\\qquad \\ 2=a_0+3a_1+9a_2 +27a_3 \\\\\n",
-    "(x,y)&=(2,-2)\\qquad\\longrightarrow\\qquad 3=a_0+a_1+a_2+a_3\\\\\n",
-    "(x,y)&=(3,-5)\\qquad\\longrightarrow\\qquad 2=a_0-4a_1+16a_2-64a_3\\\\\n",
-    "(x,y)&=(4,0)\\qquad\\longrightarrow\\qquad -2=a_0+2a_1+4a_2+8a_3\n",
+    "(x,y)&=(1,3)\\qquad\\longrightarrow\\qquad \\ 3=a_0+a_1+a_2+a_3 \\\\\n",
+    "(x,y)&=(2,-2)\\qquad\\longrightarrow\\qquad -2=a_0+2a_1+4a_2+8a_3\\\\\n",
+    "(x,y)&=(3,-5)\\qquad\\longrightarrow\\qquad -5=a_0-3a_1+9a_2-27a_3\\\\\n",
+    "(x,y)&=(4,0)\\qquad\\longrightarrow\\qquad 0=a_0+4a_1+16a_2+64a_3\n",
     "\\end{align}"
    ]
   },

From a42ba8daa98e73dca755371e0d988efc42a9d663 Mon Sep 17 00:00:00 2001
From: Ravi Ranjan <65977290+RanjanRavi2398@users.noreply.github.com>
Date: Sun, 20 Aug 2023 19:26:52 +0530
Subject: [PATCH 2/2] Update Chapter 1 - Linear Equation System.ipynb

updating equation of Visualisation of An Inconsistent System
---
 Chapter 1 - Linear Equation System.ipynb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Chapter 1 - Linear Equation System.ipynb b/Chapter 1 - Linear Equation System.ipynb
index c2f61ed..16cf869 100644
--- a/Chapter 1 - Linear Equation System.ipynb	
+++ b/Chapter 1 - Linear Equation System.ipynb	
@@ -413,7 +413,7 @@
     "\n",
     "\\begin{align}\n",
     "z&=1-x-y\\\\\n",
-    "z&=\\frac{x}{2}-\\frac{y}{2}+1\\\\\n",
+    "z&=\\frac{x}{2}-\\frac{y}{2}-1\\\\\n",
     "z&=2x-1\n",
     "\\end{align}"
    ]
@@ -429,7 +429,7 @@
     "Z = 1 - X - Y\n",
     "mlab.mesh(X, Y, Z,colormap=\"spring\")\n",
     "\n",
-    "Z = X/2 - Y/2 + 1\n",
+    "Z = X/2 - Y/2 - 1\n",
     "mlab.mesh(X, Y, Z,colormap=\"summer\")\n",
     "\n",
     "Z = 2*X - 1\n",