Question 12 (1 point each). For each of the following statements circle T if it's true or circle F if it's false. No justification is required. 1) The span of 4 vectors can have dimension 3. T F 2) The span of 3 vectors can have dimension 4. T F 3) If a homogeneous linear system has more unknowns than equations, then it must have infinitely many solutions. T F 4) If B has a column of zeros, then so does AB if this product is defined. T F 5) If A is a square matrix, and if the linear system A.E - b has a unique solution, then the linear system AT = c also must have a unique solution. T F 6) If A and B are row equivalent matrices, then the linear systems AT = 0 and BE = 0 have the same solution set. T F 7) Let A, B, C be n x n matrices. The determinant of ABC is det(A) det(B) det (C). T F 8) If A? = I, then det(A) is either 1 or -1. T F 9) The dimensions of the column space and the row space for an m x n matrix A can be different. T F 10) Let vi, 12, us be vectors in R" such that v3 - 2vj + 302. The matrix A whose columns are the three vectors vi, 12, us is invertible. T F