Hello everyone!(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Is this a linear system of equations?

**Physics Forums | Science Articles, Homework Help, Discussion**