Hello everyone, I would like to confirm my understanding of these two problems because I believe I have the answer, but I may be incorrect.
For the first question, I know that there can be at most 3 linearly independent vectors within A, which would cause the solution space to be at most 2, or nullity = 2. Given that fact, The statement that there could be 3 linearly independent solutions to Ax = 0 is false.
For the second question, the solution space could either be nothing (no solution exists) because the matrix could be filled with 0's, or infinite because of there are more columns than rows, indicating at least one free variable.
I would appreciate any feedback!