Can a homogeneous system of equations be inconsistent?

Since a homogeneous system always has a solution (the trivial solution), it can never be inconsistent. Thus a homogeneous system of equations always either has a unique solution or an infinite number of solutions.

Is system of equations which is homogeneous always have solution?

A homogeneous system of linear equations is one in which all of the constant terms are zero. A homogeneous system always has at least one solution, namely the zero vector.

Which system is always consistent?

Homogeneous system of linear equations is always consistent.

Is a non homogeneous system always consistent?

The only two options for a homogeneous system of equations is either a unique solution (trivial solution) or infinitely many solutions. So the system is always consistent due to the presence of a trivial solution. If rank of co-efficients matrix = number of unknowns (unique solution which is the trivial solution).

What makes a linear system consistent?

A system of two linear equations can have one solution, an infinite number of solutions, or no 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 .

What is always true of the solution set for a homogeneous system of equations?

What is always true of the solution set for a homogeneous system of equations? The solution set for a homogeneous system of equations will always be the zero vector.

What is a consistent system of equations?

A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions. 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 .

Is the system consistent or inconsistent?

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. If a system has no solution, it is said to be inconsistent .

How do you tell if a system of equations has infinitely many?

Conditions for Infinite Solution The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

How do you know if a system is homogeneous?

In general, the equation AX=B representing a system of equations is called homogeneous if B is the nx1 (column) vector of zeros. Otherwise, the equation is called nonhomogeneous.

Is the system of equations consistent?

Systems of equations can be classified by the number of solutions. 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 .

How many solutions does a homogeneous system of equations have?

The only two options for a homogeneous system of equations is either a unique solution (trivial solution) or infinitely many solutions. So the system is always consistent due to the presence of a trivial solution. If rank of co-efficients matrix = number of unknowns (unique solution which is the trivial solution).

What is the difference between a consistent system and homogeneous system?

A consistent system is one in which there is at least one solution to that system. In a homogenous system of equations, all are set equal to zero. Suppose we have an equation A x = b, where A is the coefficient matrix and b is…

Which system of linear equations is always consistent?

Homogeneous system of linear equations is always consistent. Homogeneous system of linear equations is always consistent. x=0,y=0 is always a solution of the homogeneous system of equations with unknowns x and y, then which of the following statement is true?