If a matrix is not invertible, can I say the matrix has many solutions? Or is the matrix has many solutions as well as the possibility or no solutions? And so if a matrix is invertible, the system of equations will definitely only have one unique solution?

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Well, think about it. If the matrix is not invertible, what does that say about it's determinant?

If it's invertible, we know the only solution to Ax = 0 is the trivial solution

And are you talking about homogeneous or non homogeneous?

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