- #1
nde
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Hello everyone!
I have a question on whether a system of equations can be classified as linear. I have the following matrix:[itex]
\begin{equation}
\left[ \begin{array}{c} S_t(1) \\ S_t(2) \\ \vdots \\ S_t(\omega_N) \end{array} \right] =
\begin{bmatrix} f(x_1, x_2, 1) & f(x_2, x_3, 1) & \cdots & f(x_i, x_{i+1}, 1) \\
f(x_1, x_2, 2) & f(x_2, x_3, 2) & \cdots & f(x_i, x_{i+1}, 2) \\
\vdots & \vdots & \ddots & \vdots \\
f(x_1, x_2, \omega_N) & f(x_2, x_3, \omega_N) & \cdots & f(x_i, x_{i+1}, \omega_N) \\
\end{bmatrix}
\times
\left[ \begin{array}{c} S_1 \\ S_2 \\ \vdots \\ S_i \end{array} \right]
\label{equationsystem}
\end{equation}
[/itex]where [itex] f(x_i, x_{i+1}, \omega_N) [/itex] is a non-linear function containing two exponential terms and [itex]S_i[/itex] is unknown. Does this system of equations qualify as linear if I know [itex]x_i, x_{i+1}[/itex] and [itex]\omega_N[/itex] and plug it into [itex] f(x_i, x_{i+1}, \omega_N) [/itex] to yield a numerical value (real number)?
If this is true, I should be able to figure out [itex]S_i[/itex] by taking the inverse of the function marix and multiplying both sides with it.
I greatly appreciate your input. Thank you in advance for taking the time to answer this.
Kind regards.
I have a question on whether a system of equations can be classified as linear. I have the following matrix:[itex]
\begin{equation}
\left[ \begin{array}{c} S_t(1) \\ S_t(2) \\ \vdots \\ S_t(\omega_N) \end{array} \right] =
\begin{bmatrix} f(x_1, x_2, 1) & f(x_2, x_3, 1) & \cdots & f(x_i, x_{i+1}, 1) \\
f(x_1, x_2, 2) & f(x_2, x_3, 2) & \cdots & f(x_i, x_{i+1}, 2) \\
\vdots & \vdots & \ddots & \vdots \\
f(x_1, x_2, \omega_N) & f(x_2, x_3, \omega_N) & \cdots & f(x_i, x_{i+1}, \omega_N) \\
\end{bmatrix}
\times
\left[ \begin{array}{c} S_1 \\ S_2 \\ \vdots \\ S_i \end{array} \right]
\label{equationsystem}
\end{equation}
[/itex]where [itex] f(x_i, x_{i+1}, \omega_N) [/itex] is a non-linear function containing two exponential terms and [itex]S_i[/itex] is unknown. Does this system of equations qualify as linear if I know [itex]x_i, x_{i+1}[/itex] and [itex]\omega_N[/itex] and plug it into [itex] f(x_i, x_{i+1}, \omega_N) [/itex] to yield a numerical value (real number)?
If this is true, I should be able to figure out [itex]S_i[/itex] by taking the inverse of the function marix and multiplying both sides with it.
I greatly appreciate your input. Thank you in advance for taking the time to answer this.
Kind regards.
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