The fundamental theorem of linear algebra states If A is a n x n matrix, then the following statements are equivalent 1.

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The fundamental theorem of linear algebra states
If A is a n x n matrix, then the following statements areequivalent
1. det(A) does not equal 0
2. A can be written as the product of elementary matrices
3. A is row equivalent to In
4. Ax = 0 has only the trivial solution
5. Ax = b has a unique solution for every n x 1 column matrixb
6. A is invertible