[tex]\spadesuit[/tex] Hei! [tex]\spadesuit[/tex]
Har et lite problem her, hvordan løser jeg denne?
Solve the system of linear equations by Gauss-Jordan elimination.
[tex]\begin{pmatrix} 2 & -1-i \\ -1+i & 1 \end{pmatrix} \begin{pmatrix}x\\y \end{pmatrix} = \begin{pmatrix}0\\0\end{pmatrix}[/tex]
[tex]\triangleright[/tex] Mvh [tex]\varepsilon[/tex]va [tex]\clubsuit[/tex]
Gauss-Jordan eliminasjon
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- Weierstrass
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Skriver opp utvidet koeffisientmatrise
[tex] \begin{pmatrix}2 & -1-i & 0\\ -1+i & 1 & 0 \end{pmatrix} \ \~ \ \begin{pmatrix}1 & - \frac{1+i}2 & 0\\ -1+i & 1 & 0 \end{pmatrix} \begin{matrix}\frac{R1}2 \\ R2\end{matrix} \ \~ \ \begin{pmatrix}1 & - \frac{1+i}2 & 0\\ 0 & 1 + \frac{1+i}2 \cdot (-1+i) & 0 \end{pmatrix} \begin{matrix}R1 \\ R2 - R1(-1+i)\end{matrix} \ \~ \ \\ \begin{pmatrix}1 & - \frac{1+i}2 & 0\\ 0 & 0 & 0 \end{pmatrix} \~ \[/tex]
Dette gir:
[tex]x = \frac{1+i}2 y[/tex]
[tex] \begin{pmatrix}2 & -1-i & 0\\ -1+i & 1 & 0 \end{pmatrix} \ \~ \ \begin{pmatrix}1 & - \frac{1+i}2 & 0\\ -1+i & 1 & 0 \end{pmatrix} \begin{matrix}\frac{R1}2 \\ R2\end{matrix} \ \~ \ \begin{pmatrix}1 & - \frac{1+i}2 & 0\\ 0 & 1 + \frac{1+i}2 \cdot (-1+i) & 0 \end{pmatrix} \begin{matrix}R1 \\ R2 - R1(-1+i)\end{matrix} \ \~ \ \\ \begin{pmatrix}1 & - \frac{1+i}2 & 0\\ 0 & 0 & 0 \end{pmatrix} \~ \[/tex]
Dette gir:
[tex]x = \frac{1+i}2 y[/tex]