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I need to find solutions to a matrix whose determinant is 0, and I have already shown that the matrix has infinitely many solutions. Can anyone explain me how to find the form of the solutions?

(solutions should come with a parameter that is free to choose, but there are some complicated constants in front of that free parameter and I don't know how to get to them).

Many thanks!

J. W. Tanner
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  • Welcome to Mathematics Stack Exchange. Please clarify what you mean by solutions to a matrix – J. W. Tanner Dec 17 '19 at 15:14
  • Are you looking for a basis of some kind? – Annapox Dec 17 '19 at 15:16
  • The way that you phrased your question is incorrect. A matrix who is not square or who has determinant zero does not have an inverse. You can still possibly find the set of all $x$ such that $Ax=b$ however but that is not the same thing as finding an inverse. The usual strategy being to find the nullspace of $A$ and a particular solution, the solution set being the set of all possible sums of the particular solution with an element of the nullspace. You might choose to accomplish this by row reduction of the augmented matrix $[A\mid b]$. – JMoravitz Dec 17 '19 at 15:27

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