From 66f7a9b8b37b4cf22f55a301243a91f1f76855cc Mon Sep 17 00:00:00 2001
From: Andre Henriques <andr3h3nriqu3s@gmail.com>
Date: Fri, 3 Nov 2023 16:16:24 +0000
Subject: [PATCH] Fix cw.tex

---
 cw/cw.tex | 36 ++++++++++++++++++++++++++++++++----
 1 file changed, 32 insertions(+), 4 deletions(-)

diff --git a/cw/cw.tex b/cw/cw.tex
index c220d99..e86d269 100644
--- a/cw/cw.tex
+++ b/cw/cw.tex
@@ -7,6 +7,7 @@
 \usepackage{pdfpages}
 \usepackage{float}
 \usepackage{amsmath}
+\usepackage{systeme}
 
 \usepackage{graphicx}
 \graphicspath{ {../images for report/} }
@@ -105,16 +106,43 @@
 	\section*{7}
 	\subsection*{7.1}
 	$$v1 = (137, 312), v2 = (215, -187)$$
-	$$mat =   \begin{pmatrix}
+	$$u1 = (1975,438), u2 = (7548, 1627)$$
+
+	$$B =   \begin{pmatrix}
 			137 & 312 \\
 			215 & -187 \\
 			\end{pmatrix}$$
-	$$det(L)=|det(mat)|=|-92699|=92699$$
+	$$U =   \begin{pmatrix}
+			1975 & 438\\ 
+			7548 & 1627\\
+			\end{pmatrix}$$
+
+	A:
+
+	$$det(L)=|det(B)|=|-92699|=92699$$
 
 	$$H(B)=(\frac{det(L)}{\|v1\|\times\|v2\|})\times\frac{1}{n}=(\frac{92699}{\sqrt{v1_1^2 + v1_2^2}\times\sqrt{v2_1^2 + v2_2^2}})\times\frac{1}{2}=$$
-	$$=\frac{92699}{2\times\sqrt{9427678922}}\approx0.477356$$
+	$$=\frac{92699}{2\times\sqrt{9427678922}}\approx0.477356\approx0.48$$
 
-	
+	$$H(U)=(\frac{det(L)}{\|u1\|\times\|u2\|})\times\frac{1}{n}=(\frac{92699}{\sqrt{u1_1^2 + u1_2^2}\times\sqrt{u2_1^2 + u2_2^2}})\times\frac{1}{2}=$$
+	$$=\frac{92699}{2\times\sqrt{243990681350077}}≈0.00296728\approx0.0030$$
+
+	B:
+	$$w = (30548, 6642)$$
+	$$\systeme{
+		30548=137t_1 + 312t_2,
+		6641=215t_1 + -187t_2
+	}=\systeme{
+		a = \frac{7784468}{92699},
+		b = \frac{5658003}{92699}
+	}=\systeme{
+		a \approx 83.98,
+		b \approx 61.04
+	}=\systeme{
+		a \approx 84,
+		b \approx 61
+	}
+	$$