There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.
No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.
She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.
zero solutions. If you plot these two lines, you will see that they are parallel and do not intersect.
Let the number of unknowns be N. The solution space may have N, N-1, ..., 0 dimensions or may not exist. If a solution exists and the dimension of the solution space is 0, then there is exactly one solution,. If the dimension of the solution space > 0, then there are infinitely many solutions.
There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.
A homogeneous system of equations will be inconsistent if it has a non-trivial solution, meaning that the variables can be simultaneously set to values other than zero. This can occur when the number of equations is greater than the number of unknowns in the system.
No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.
Principle stating that older rock layers are beneath younger rock layers.
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
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
No, solid solutions also exist.
No, solutions can exist in different states of matter, not just in the liquid state. Solutions can exist in the solid, liquid, or gas state depending on the solvent and solute involved in the mixture.
She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.
zero solutions. If you plot these two lines, you will see that they are parallel and do not intersect.
Let the number of unknowns be N. The solution space may have N, N-1, ..., 0 dimensions or may not exist. If a solution exists and the dimension of the solution space is 0, then there is exactly one solution,. If the dimension of the solution space > 0, then there are infinitely many solutions.
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