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What is the difference between nonlinear and linear equations?
== Linear equations are those that use only linear functions and operations. Examples of linearity: differentiation, integration, addition, subtraction, logarithms, multiplication or division by a constant, etc. Examples of non-linearity: trigonometric functions (sin, cos, tan, etc.), multiplication or division by variables.
What is the meaning of a system of linear equation that are dependent?
It means that at least one of the equations can be expressed as a linear combination of some of the other equations. A linear combination of equations is the addition (or subtraction) of equations. And since an equation can be added several times, it includes multiples of equations. For example, if you have x + 2y = 3 and 2x + y = 4 Then adding 2 times the first and 3 times the second gives 8x + 7y = 18 This is, therefore, dependent on the other 2. If you have n unknown variables, there will be a unique solution if, and only if, you must have a set of n independent linear equations.
Methods on system of linear equations?
Lety be the column vector the dependent variable,M be the matrix of coefficients, andx be the column vector of variablesso that the system of equations may be represented by y = Mx.Then the solution set is obtained by left-multiplying both sides by M^-1that is x = M^-1*y
Where the given equations are not linear?
Equations are not linear when they are quadratic equations which are graphed in the form of a parabola
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
