salistoun said:Hi all,
How do u go about doing this question?
x - 2y +z =4
y- z =3
(a^2 - a - 2)z = a+1
Determine values of a for which the system has no solution, one solution and many solutions
Stephen
A nonhomogeneous system of linear equations is a set of equations in which the constant term is not equal to zero. This means that the equations do not have a common solution and cannot be solved by setting all variables equal to zero.
In a homogeneous system, all of the constant terms are equal to zero. This means that the equations have a common solution and can be solved by setting all variables equal to zero. In a nonhomogeneous system, at least one of the constant terms is not equal to zero, making it more complex to solve.
The best method for solving a nonhomogeneous system of linear equations is through the use of Gaussian elimination or matrix operations. These methods involve transforming the equations into a simpler form and solving for the variables.
Yes, a nonhomogeneous system of linear equations can have a unique solution if the equations are consistent (have a common solution) and the number of equations is equal to the number of variables. In this case, the solution can be found using Gaussian elimination or matrix operations.
Nonhomogeneous systems of linear equations are used in many areas of science and engineering, such as predicting population growth, analyzing chemical reactions, and modeling financial markets. They can also be used to solve problems in physics, biology, and other fields where variables are related to one another.