How do you know if a matrix equation has infinite solutions?
How do you know if a matrix equation has infinite solutions?
Finding if a matrix equation has an infinite solution or not:
A matrix equation or the system of equations of the form may have one solution, no solution, and infinitely many solutions based on the behavior of free variables in the reduced row-echelon form of a matrix.
Condition of a matrix for having infinite solutions:
There will be an infinite number of solutions if and only if there is at least one solution, and also there are an infinite number of solutions to the linear equation .
In simple words, when a system is consistent, and the number of variables is more than the number of nonzero rows in the reduced row-echelon form of the matrix, the matrix equation will have infinitely many solutions.
Hence, a matrix has an infinite solution if the number of variables is more than the number of nonzero rows in the reduced row-echelon form of the matrix.
Finding if a matrix equation has an infinite solution or not:
A matrix equation or the system of equations of the form may have one solution, no solution, and infinitely many solutions based on the behavior of free variables in the reduced row-echelon form of a matrix.
Condition of a matrix for having infinite solutions:
There will be an infinite number of solutions if and only if there is at least one solution, and also there are an infinite number of solutions to the linear equation .
In simple words, when a system is consistent, and the number of variables is more than the number of nonzero rows in the reduced row-echelon form of the matrix, the matrix equation will have infinitely many solutions.
Hence, a matrix has an infinite solution if the number of variables is more than the number of nonzero rows in the reduced row-echelon form of the matrix.
