Fix cw.tex
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Andre Henriques 2023-11-03 16:16:24 +00:00
parent d691b2c0b7
commit 66f7a9b8b3

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@ -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
}
$$