Mark the following statements True or False If the equation

Mark the following statements True or False. If the equation Ax vector = 0 vector has only the trivial solution, then A is row equivalent to the n times n identity matrix. If the columns of A span R^n, then the columns are linearly independent. If A is an n times n matrix, then the equation Ax vector = b vector has at least one solution for each b vector in R^n. If the equation Ax vector = 0 vector has a nontrivial solution, then A has fewer than n pivots positions. If A^T is not invertible, then A is not invertible.

Solution

1,2,3 are trues