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Word problems on ages. Pythagorean theorem word problems. Percent of a number word problems. Word problems on constant speed. Word problems on average speed. A system with intersecting lines is considered consistent because it has at least one solution, and independent because it has exactly one solution.
This system would be both independent and consistent. The lines completely overlap. When solving a system of coincident lines , the resulting equation will be without variables and the statement will be true.
This is called a consistent -dependent system. 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. Definitions: If the two equations describe lines that intersect once, the system is independent and consistent. If the two equations describe parallel lines , and thus lines that do not intersect, the system is independent and inconsistent. When a system of equations has no solution, it is called inconsistent. If a system of equations is inconsistent , then when we try to solve it, we will end up with a statement that makes no sense, and if we observe the graphs of the equations involved, we will see that they never intersect.
How do you know if a matrix is inconsistent or consistent? Category: science physics. The way you figure out whether or not an augmented matrix is consistent is by first row reducing it. If , after row reducing, you see something like this: the matrix is inconsistent. Notice the last row. What makes a matrix consistent? Linear systems.
What does it mean to be consistent? What is the rank of a matrix? How do you know if a system has infinite solutions? What do you mean by inconsistent? What is a unique matrix? Is my reasoning correct? Show 1 more comment. Active Oldest Votes. H Green. Add a comment. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.
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