What makes a system have infinite solutions

But it is not impossible that an equation cannot have more than one solution or infinite number of solutions or no solutions at all. Having no solution means that an equation has no answer whereas infinite solutions of an equation means that any value for the variable would make the equation true. The total number of variables in an equation determines the number of solutions it will produce. And on the basis of this, solutions can be grouped into three types, they are:.

Unique Solution which has only 1 solution. No Solutions having no solutions. Infinite Solutions having many solutions. But how would you know if the solution to your solved equation is an infinite solution?

Well, there is a simple way to know if your solution is an infinite solution. An infinite solution has both sides equal. Infinite represents limitless or unboundedness. An equation will produce an infinite solution if it satisfies some conditions for infinite solutions. An infinite solution can be produced if the lines are coincident and they must have the same y-intercept. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search.

Can someone please tell me what a matrix looks like when there is infinite solutions, unique solution and no solutions. I have been searching the internet and I cannot find a straightforward answer of what the matrix should look like.

The question I am faced with is that I have a variable in a 3x3 matrix and I have to get the values of that variable when there is no solution, infinite and unique solution. The approach generalizes to larger systems. If, by clever combinations of the equations, you obtain always-false or always-true equations, then the system is impossible or indeterminate, respectively. There is a systematic method to combine the equations in a way that progressively forms smaller systems, called Gaussian elimination.

It will transform a square system in a triangular one. If at some stage all remaining coefficients are zero, then you are in one of these singular cases. Sign up to join this community. The best answers are voted up and rise to the top.

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As you can see the code gives us an error suggesting there is no solution to the matrix. As you can see, the final row of the row reduced matrix consists of 0. This means that for any value of Z, there will be a unique solution of x and y, therefore this system of linear equations has infinite solutions.

As you can see we get a different type of error from this code. It states that the matrix is ill-conditioned and that there is a RuntimeWarning. This means that the computer took to long to find a unique solution so it spat out a random answer.

When RuntimeWarings occur, the matrix is likely to have infinite solutions.