Table of Contents
- 1 Does consistent mean unique solution?
- 2 What is unique solution in math?
- 3 What is the difference between consistent and inconsistent solution?
- 4 What is consistent solution?
- 5 Are trivial solutions consistent?
- 6 What is meant by trivial solution?
- 7 How do you know if a system has a unique solution?
- 8 How do you know if a matrix has one unique solution?
Does consistent mean unique solution?
i) If both the lines intersect at a point, then there exists a unique solution to the pair of linear equations. In such a case, the pair of linear equations is said to be consistent.
What is unique solution in math?
In a set of linear simultaneous equations, a unique solution exists if and only if, (a) the number of unknowns and the number of equations are equal, (b) all equations are consistent, and (c) there is no linear dependence between any two or more equations, that is, all equations are independent.
What is called a unique solution?
By the term unique solution, one mean to say that only one specific solution set exists for a given equation. So, if we have two equations, then unique solution will mean that there is one and only point at which the two equations intersect.
What is the difference between trivial and unique solution?
Unique solution- has an exact solution (such as a POI of 2 intersecting lines) Trivial solution- when 0 needs to equal the zero vector in Ax=0vector. Non-Trivial-? Perhaps when 0 does not equal the zero vector in Ax=0.
What is the difference between consistent and inconsistent solution?
A consistent system of equations has at least one solution, and an inconsistent system has no solution.
What is consistent solution?
If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
How do you identify a unique solution?
A nxn homogeneous system of linear equations has a unique solution if and only if its Determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions. A system has a unique solution when it is consistent and the number of variables is equal to the number of nonzero rows.
How do you know if a solution is unique?
A nxn homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions.
Are trivial solutions consistent?
1. A homogeneous equation is always consistent. The equation Ax = 0 has the trivial solution if and only if the equation has at least one free variable.
What is meant by trivial solution?
“Trivial” can also be used to describe solutions to an equation that have a very simple structure, but for the sake of completeness cannot be omitted. These solutions are called the trivial solutions. For example, consider the differential equation.
What is consistent and inconsistent in maths?
If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
What is consistent and inconsistent with example?
System of linear equations is a group of two or more linear equations having the same variables. For example, x + 2y = 14 , 2x + y = 6. If there is nothing common between the two equations then it can be called as inconsistent. But it will be called consistent if any one ordered pair can solve both the equations.
How do you know if a system has a unique solution?
A system has a unique solution when it is consistent and the number of variables is equal to the number of nonzero rows. If the rref of the matrix for the system is , the solution is the single point ( 2, 1, 3 ) or x=2, y=1, z=3
How do you know if a matrix has one unique solution?
As you can see, each variable in the matrix can have only one possible value, and this is how you know that this matrix has one unique solution Let’s suppose you have a system of linear equations that consist of: which impossible, 0 cannot equal -3. Therefore this system of linear equations has no solution.
What is the difference between consistent and inconsistent equations?
Transcript A consistent system of equations has at least one solution, and an inconsistent system has no solution. Watch an example of analyzing a system to see if it’s consistent or inconsistent. Created by Sal Khan and Monterey Institute for Technology and Education.
When does a system have infinitely many solutions?
A system has infinitely many solutionswhen it is consistent and the number of variables is more than the number of nonzero rows in the rref of the matrix. For example if the rref is has solution set (4-3z, 5+2z, z) where z can be any real number. In this case z is called the parameter.