I am in a linear algebra and differential equations course and have recently been learning how to find a basis for a nullspace, row space, or column space. However, I am EXTREMELY confused by a solution to a question in my textbook. The question asks to find the basis for the null space of a particular matrix. For the question at hand, the determinant is zero, which of course means that it is invertible. However, I'm confused as to why this means that there is no basis for this nullspace -- there is no relevant explanation in my text as far as I can tell. Thank you to anyone who can help solve this problem for me!