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Homogeneous system with m equations and n unknowns how to prove it has only one solution?
Wiki User
∙ 13y ago
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)
Wiki User
∙ 13y ago
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Why are systems of equations important?
A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique solution.
What is the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
What system of equations has no solution?
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
Solving the system of equations by graphing?
Graph both equations on the same graph. Where they intersect is the solution to the system of equations
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
What is cramer rule?
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
What is a system of linear equations in two variables?
They are a set of equations in two unknowns such that any term containing can contain at most one of the unknowns to the power 1. A system of linear equations can have no solutions, one solution or an infinite number of solutions.
Why are systems of equations important?
A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique solution.
Solve the system using elimination 3x -9y equals 3?
Solving equations in two unknowns requires two independent equations. Since you have only one equation there is no solution.
What is a solution to a system of equations graphically?
Graphically, it is the point of intersection where the lines (in a linear system) intersect. If you have 2 equations and two unknowns, then you have a 2 lines in a plane. The (x,y) coordinates of the point where the 2 lines intersect represent the values which satisfies both equations. If there are 3 equations and 3 unknowns, then you have lines in 3 dimensional space. If all 3 lines intersect at a point then there is a solution to the system. With more than 3 variables, it is difficult to visualize more dimensions, though.
Can you solve the system using elimination 3x plus 9y equals 3?
No. Solving equations in two unknowns requires two independent equations. Since you have only one equation there is no solution.
How many types of solutions of a system of two linear equations in two unknowns can exist?
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.
What is y equals 2x plus 1 and y equals 2x-3?
A pair of simultaneous equations in two unknowns which are inconsistent - in the sense that there is no solution that simultaneously satisfies both equations. Graphically, the equations are those of two parallel lines (slope = 2). Since, by definition, they cannot meet there is no solution to the system.
What is a system of linear equations that has no solution?
there is no linear equations that has no solution every problem has a solution
Does any homogeneous system have nontrivial solution?
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
A system of equations with exactly one solution?
A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.
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.
