f) If an n x n matrix A has n pivot positions, then the reduced echelon form of A is the n x n identity matrix. 9) If A is an m xn matrix, if the equation Ax = b has at least two different solutions,...

Mark each statement True or False. Justify each answer, (if true, cite appropriate
facts or theorems. If false, explain why or give a counterexample that shows why
the statement is not true in every case).

Extracted text: f) If an n x n matrix A has n pivot positions, then the reduced echelon form of A is the n x n identity matrix. 9) If A is an m xn matrix, if the equation Ax = b has at least two different solutions, and if the equation Ax = c is consistent, then the equation Ax = c has many solutions. h) If u and v are in Rm, then -u is in Span {u, v}. i) Suppose that v,, v2, and vz are in RS, v2 is not a multiple of v,, and vz is not a linear combination of v, and v2. Then {v1, v2, V3} is linearly independent. j) If A is an m x n matrix with m pivot columns, then the linear transformation x - Ax is a one-to-one mapping.