- #1

- 2

- 0

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.

Last edited: