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Find the ordered quintuplet  that satisfies the system of equations

\(a+2b+3c+4d+5e=47 \)

\(2a+3b+4c+5d+e=15\)

\(3a+4b+5c+d+2e=3\)

\(4a+5b+c+2d+3e=26\)

\(5a+b+2c+3d+4e=20\)

 Apr 14, 2024
 #1
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We can write the equation as

 

\[
\begin{pmatrix}
1 & 2 & 3 & 4 & 5 \\
2 & 3 & 4 & 5 & 1 \\
3 & 4 & 5 & 1 & 2 \\
4 & 5 & 1 & 2 & 3 \\
5 & 1 & 2 & 3 & 4
\end{pmatrix}
\begin{pmatrix}
a \\ b \\ c \\ d \\ e
\end{pmatrix}
=
\begin{pmatrix}
47 \\ 15 \\ 3 \\ 26 \\ 29
\end{pmatrix}
.
\]
 

Inverting the matrix, we get the solution (a,b,c,d,e) = (-5, 4, 14, 3, -2).

 Apr 14, 2024

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