There are 8 statements given below with a number to the left of each statement. Create anumber from these numbers by selecting all of the statements that are true. For example,if the only true statements are 2, 3 and 5, then create the number 235, and give this asyour answer.
1. Suppose A is an m x n matrix and b is an m x 1 column vector. If the homogeneous system Ax =0 has infinitely many solutions, then the system Ax = b has infinitely many solutions.
2. Suppose A is an m x n matrix and b is an m x 1 column vector. The system Ax = b has a unique solution if and only if the homogeneous system Ax =0 has only the trivial solution.
3. Every homogeneous system of linear equations is consistent.
4. A system of linear equations either has no solution, one solution, or infinitely many solutions.
5. There are systems of linear equations with exactly 3 solutions.
6. If a set is linearly independent, and it has 2 or more vectors in it, then the set will stillbe linearly independent after you remove a vector from it.
7. There is a linearly independent subset of ?R^4 that contains 5 vectors.
8. There is a linearly independent subset of ?R^4 that contains only 1 vector.