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Find a matrix A that is not invertible and b such that Ax equals b has a unique solution?
A matrix with a row or a column of zeros cannot have an inverse.
Proof:
Let A denote a matrix which has an entire row or column of zeros. If B is any matrix, then AB has an entire rows of zeros, or BA has an entire column of zeros. Thus, neither AB nor BA can be the identity matrix, so A cannot have an inverse, or A cannot be invertible.
Since A is not invertible, then Ax = b has not a unique solution.
What else can I help you with?
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row reduce the matrix in question and see if it has any free variables. if it does then it has many solution's. If not then it only has one unique solution. which is of course the trivial solution (0)
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