If the rows of an m-by-n matrix A are linearly independent, then Ax = b is always
solvable.
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If the rows of an m-by-n matrix A are linearly independent, then the solution of Ax
= b, if it exists, is always unique.
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If the columns of an m-by-n matrix A are linearly independent, then Ax = b is
always solvable.
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For n-by-n real symmetric matrices A and B, AB and BA always have the same
eigenvalues.
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For n-by-n matrices A and B with B invertible, AB and BA have the same
eigenvalues.
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Two diagonalizable matrices A and B with the same eigenvalues and eigenvectors
must be the same
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If the columns of a matrix are dependent, so are the rows of the matrix.
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