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What is independent system?
Independence:The equations of a linear system are independentif none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.Consistency:The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.Homogeneous:If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.
What are the three types of systems of linear equations and their characteristics?
Independence:The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.Consistency:The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.Homogeneous:If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.
What is the formula for system of equations?
They are formed by two expressions that are equal to each other.
Is the kinematics equation true if acceleration is not constant?
Kinematics does not require constant acceleration. There are different equations for different situations. So some of the equations will be valid even when the acceleration is not constant.
What is the constant k in directs and inverse equations?
The constant could be any number.
How to find the equilibrium point in a system?
To find the equilibrium point in a system, set the equations representing the system to zero and solve for the variables. The equilibrium point is where all variables remain constant over time.
What is a constant value that are not coefficients of variables to equations?
parameters
What are the common characteristic between simultaneous linear equations in 2 unknowns which have no solutions?
The coefficients and constant in one of the equations are a multiple of the corresponding coefficients and constant in the other equation.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
If a system of equations is inconsitient how many solutions will it have?
If a system of equations is inconsistent, there are no solutions.
Why temperature is constant for castigliano theorem?
Castiglino's Theorem uses the principle of minimum potential energy to find an equation or system of equations for the deflection of a configuration. Therefore, the energy of the system must be constant during the analysis. When a temperature change is observed, the system absorbs energy from the surrounding resulting in thermal expansion.
If a system of equations is independent how many soultions will it have?
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
