Question: Let A be an n x n matrix. Consider the following statements. (i) Ax = 0 has nontrivial solutions. (ii) A can be expressed

Let A be an n x n matrix. Consider the following statements.

Let A be an n x n matrix. Consider the following statements. (i) Ax = 0 has nontrivial solutions. (ii) A can be expressed as a product of elementary matrices. (ii) 1 = 0 is an eigenvalue of A. (iv) The reduced row-echelon form of A is Ip. (v) det(4) # 0 (vi) A is NOT diagonalizable. Determine which of the above statements are equivalent to A being invertible (1) or NOT equivalent to A being invertible (2).

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