0
x+y=0
2x+2y=0
This homogeneous system has infinitely many non-trivial solutions.
If you are looking for exactly one non-trivial solution, no such system exists. the system may or may not have non trivial solution. if number of variables equal to number of equations and given matrix is non singular then non trivial solution does not exist
What else can I help you with?
Must solutions to systems of linear equalities satisfy both equalities?
Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.
What is any and all values of the variable that satisfies an equation inequality system of equations or system of inequalities?
They make up the solution set.
If a system has an infinite number of solutions does it follow that any ordered pair is a solution?
No, this is not necessarily the case. A function can have an infinite range of solutions but not an infinite domain. This means that not every ordered pair would be a solution.
What is the solution of the system of equations y-2x 5 -5y10x 20?
Without any equality signs the given expressions can't be considered as equations.
Can you solve system of equations by graphing?
Yes you can, if the solution or solutions is/are real. -- Draw the graphs of both equations on the same coordinate space on the same piece of graph paper. -- Any point that's on both graphs, i.e. where they cross, is a solution of the system of equations. -- If both equations are linear, then there can't be more than one such point.
Is salt a solution or a homogeneous solution?
A solution of any sort is a homogeneous mixture.
What is complementary solution in differential equations?
In differential equations, the complementary solution (or homogeneous solution) is the solution to the associated homogeneous equation, which is obtained by setting the non-homogeneous part to zero. It represents the general behavior of the system without any external forcing or input. The complementary solution is typically found using methods such as characteristic equations for linear differential equations. It is a crucial component, as the general solution of the differential equation combines both the complementary solution and a particular solution that accounts for any non-homogeneous terms.
What does a solution and a homogeneous mixture have in common?
Any phase is distinct.
What is part of a system having uniform composition and properties?
A homogeneous system is part of a system with uniform composition and properties, where the components are evenly distributed and indistinguishable at a macroscopic level. Examples include a well-mixed solution or a single-phase alloy.
Homogeneous system with m equations and n unknowns how to prove it has only one solution?
row reduce the matrix in question and see if it has any free variables. if it does then it has many solution's. If not then it only has one unique solution. which is of course the trivial solution (0)
What does it mean to say that a solution is homogeneous?
Homogeneous means that a material is the same throughout. Samples taken from any part of the material will be identical to one another. Elements and compounds are homogeneous pure substances. Solutions are homogeneous mixtures.
Why are homogeneous equations never inconsistent?
Homogeneous equations are never inconsistent because they always have at least one solution: the trivial solution, where all variables are set to zero. Since the definition of inconsistency involves the absence of solutions, the existence of this trivial solution guarantees that homogeneous equations will always have a solution set, making them consistent by nature. Additionally, any linear combination of solutions to a homogeneous equation will also be a solution, further reinforcing their consistent nature.
Is salt solution a homogeneous or a heterogeneous?
Each crystallic particle is pure NaCl, homogeneous.
Why is a sugar water solution a homogeneous mixture?
I think you mean a homogeneous mixture. Its because sugar is completely dissolved in water, so it will not be visible anymore, therefore, they become with only one phase or as you call it... a 'clear solution'
What words mean same and describes how molecules are distributed a solution?
The words that mean the same and describe how molecules are distributed in a solution are "homogeneous" and "uniform." A homogeneous solution has a consistent composition throughout, meaning the molecules are evenly distributed. This uniform distribution ensures that any sample taken from the solution will have the same concentration of solute.
Examples of a homogeneous mixture?
A glass of saltwater, a solution of sugar in water, and air are examples of homogeneous mixtures. In each case, the components are evenly distributed throughout the mixture at a molecular level, resulting in a uniform appearance and properties.
What is the difference between water and a solution?
Water is a pure substance composed of H2O molecules. A solution is a homogeneous mixture composed of a solvent (like water) and one or more solutes dissolved in the solvent. In a solution, the solvent (such as water) dissolves the solutes to create a homogeneous mixture.
