Examples of linear equation

This example is from Wikipedia and may be reused under a CC BY-SA license.
We instead assume uncertainty about the values of coefficients of the linear equations of the structural model.
In fact, the commentators qualify in this way only one among the other procedures: the algorithm for solving systems of simultaneous linear equations, mentioned above.
Other problems like proportions and linear equations employed different methods appropriate to the problems.
Equation 13 is actually a set of linear equations, the unknowns of which are the flows in the resistance chords of the graph.
With a little ingenuity, instability can be avoided, at least for linear equations.
This theorem is remarkable since it says that one can solve underdetermined systems of linear equations by linear programming.
Note that, once is known, the transport equations are linear equations with variable coefficients.
This equation can also be found directly from the linear equations.
In the fir st-order approximation, we obtain a system of linear equations for the variables, denoted with super script '(1)'.
In the fir st-order approximation, we obtain a system of homogeneous linear equations for the variables with the super script (1).
If these manipulations are carried out, we obtain a set of homogeneous linear equations in the expansion coefficients of the trial functions.
Simple matrix inverting procedures are applied for the linear equations to get solutions that actually correspond to boundary points of allowable taskvelocity space.
By contrast, linear equations should suffice for the modelling of the hull, because it is not expected to undergo large displacements.
We also introduce linear equations to extend the results to certain quotient monads.
One reason might be that electromagnetism is described by a generically linear theory, in the sense that linear equations arise from basic physical principles.
These limit state equations are again replaced by equivalent linear equations.
To illustrate the approach, the solution of a set of linear equations is considered.
Another explanation is that when segregated approaches are used, standard sparse linear equations packages are often sufficient to solve the reduced linear systems.
That is, call a set of integers 'large' if it contains solutions to all partition regular systems of homogeneous linear equations.
The linear equations governing the subsequent coefficients of the series solution and detailed results for the leading axisymmetric and rotational effects are then given ($4).
It is also shown that, without neglecting the displacement current, there exist solutions of the linear equations which are also solutions of the exact equations.
In particular, it will be shown how to solve (homogeneous or non-homogeneous) linear equations, possibly with non-constant coefficients.
This algorithm involves solving large sparse systems of linear equations.
The algebraic solution of 304 coupled linear equations in 274 variables is a tedious task, even with the aid of computer algebra packages.
This also suggests that the linear equations (2.23) and (2.24), which relate the flux of fluid through the contact line to the difference in chemical potential, should be nonlinear.
Bounded solutions of scalar, almost periodic linear equations.
The correction involved the solution of a cell problem in the analytic case and the solution of a system of linear equations for the wavelet-based methodology.
Equations (6.12) represent a set of linear equations in factored form.
Some of the algorithms to be presented later are aimed at the general equation (2.25), while others are aimed at exploiting the special structure of linear equations.
Since the switching rules consist of a system of linear equations with integer coefficients, the set of rational solutions (rational coordinates) is dense in the set of solutions.
If the displacement current is neglected the exact equations are identical with the linearized ones and thus exact solutions of the linear equations are also solutions of the complete equations.
Some explicit solutions of the linear equations are obtained for plane flows and for axi-symmetric flows in which the velocity vector lies in a vertical, meridional plane.
In the area of differential equations, linear equations simply assume that rates of change follow generalized straight line functions of the variables rather than curved line functions.
Future studies may include a mathematical analysis of the relation between the proposed method and the previous methods for the minimum infinity-norm solution of a class of linear equations.
In contrast to the rule of three, the procedure for solving systems of simultaneous linear equations is described within the context of a problem dealing with the production of millets.
On diagonability and reducibility of linear equations.
Simple linear equations are taught from key stage 3.
From the
Hansard archive