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