Question: Mark each statement \(T\) or \(F\) by circling your choice and justify your answers using theory from Linear Algebra.

1. Tor \(F\) If the equation \(A x=0\) has only the trivial solution, then \(A\) is row equivalent to the \(n \times n\) identity matrix.
2. \(T\) or \(F\) If the columns of \(A\) span \(\mathbb{R}^{n}\), then the columns are linearly independent. c. \(T\) or \(F\) If \(A\) is an \(n \times n\) matrix, then the equation \(A x=b\) has at least one solution for each \(\boldsymbol{b}\) in \(\mathbb{R}^{n}\).
   d. T or \(F\) If the equation \(A x=0\) has a nontrivial solution, then \(A\) has fewer than \(n\) pivot positions.
   e. \(T\) or \(F\) If \(A^{T}\) is not invertible, then \(A\) is not invertible.
   
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