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A homogeneous system of eqs: Ax=0 will always be consistent, since x=0 is always a possible solution. However, if det(A)=0 then there will be infinite solutions, as |A|=0 implies that either no solutions or infinitely many exist, and it is impossible for no solutions to exist to Ax=0. If det(A) is non 0, then x=0 is the only solution, as |A| is not equal to 0 implies a unique solution only!(in this case x=0). Hope this helps!
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What is a homogenous systems?
A homogeneous system is one in which the components or phases are uniform and consistent throughout, meaning that the properties are the same in all parts of the system. This can apply to mixtures, materials, or equations where the composition does not vary spatially. In contrast, a heterogeneous system exhibits variations in composition or properties. Homogeneous systems are often easier to analyze mathematically due to their uniform nature.
How do you interpret the solution of a system of equations by the corresponding graph?
The solution of a system of equations corresponds to the point where the graphs of the equations intersect. If the equations have one unique point of intersection, that point represents the solution of the system. If the graphs are parallel and do not intersect, the system has no solution. If the graphs overlap and coincide, the system has infinitely many solutions.
Is zucchini bread a homogeneous mixture?
Zucchini bread is not a homogeneous mixture; it is a heterogeneous mixture. While the ingredients are combined and baked, you can still distinguish between the different components, such as pieces of zucchini, flour, and other additives. The texture and appearance vary throughout the bread, making it inconsistent in composition. Homogeneous mixtures have a uniform composition throughout, which zucchini bread does not possess.
What is complimentary function?
The complementary function, often denoted in the context of solving differential equations, refers to the general solution of the associated homogeneous equation. It represents the part of the solution that satisfies the differential equation without any external forcing terms. In the context of linear differential equations, the complementary function is typically found by solving the homogeneous part of the equation, which involves determining the roots of the characteristic equation. This solution is then combined with a particular solution to obtain the complete solution to the original non-homogeneous equation.
Is saliva a heterogeneous or homogeneous?
it is homogeneous
What is a inconsistent system?
An inconsistent system of equations is when you have 2 or more equations, but it is not possible to satisfy all of them at the same time. (E.g if you have 3 equations, but can only satisfy 2 at once, it is an inconsistent system).
If a system of equations is inconsitient how many solutions will it have?
If a system of equations is inconsistent, there are no solutions.
What describes a system of equations that has no solution?
Inconsistent.
What is a inconsistent line?
its a system of equations, with no solution
What is inconsistent system of linear equation?
It is a system of linear equations which does not have a solution.
When will a system of linear equations be inconsistent?
When the matrix of coefficients is singular.
A system of equations of two or more parallel lines is called a what?
Inconsistent
How many solutions does a system of linear equations have if it is inconsistant?
A set of equations is inconsistent, if its solution set is empty.
Which best describes a system of equations that has no solution?
An "inconsistent" set of equations. If they are all linear equations then the matrix of coefficients is singular.
How many solutions does an inconsistent system of equations have?
If a system is inconsistent it cannot have any solutions.A system of equations is considered inconsistent when the lines are parallel which means they never intersect so there are no solutions.A system is considered consistent when they intersect at one point and have one solution (Also known as an independent system of equations).Dependent Systems are when the lines coincide (the same equation) so they have an infinite number of solutions.
In solving a system of two linear equations or two functions by graphing what is meant by if the system is consistent or inconsistent?
A system of linear equations is consistent if there is only one solution for the system. Thus, if you see that the drawn lines intersect, you can say that the system is consistent, and the point of intersection is the only solution for the system. A system of linear equations is inconsistent if it does not have any solution. Thus, if you see that the drawn lines are parallel, you can say that the system is inconsistent, and there is not any solution for the system.
What are the possible solutions for a pair of linear equation?
Any system of linear equations can have the following number of solutions: 0 if the system is inconsistent (one of the equations degenerates to 0=1) 1 if the system is linearly independent infinity if the system has free variables and is not inconsistent.
