Nairdak

So you failed a course this semester in college. Or two courses. Or three. Depending on your situation, it's either having tell it all to your parents and friends, the fact that you've never failed anything in school before, or your plummeting GPA that now keeps you up at night. The damage is done, but you need to know exactly how damaging it is, and what to do to fix it?  Will you just need a band-aid or stitches? FINANCIAL AID AND SCHOLARSHIPS You may already know this, but to those freshmen who possibly don't, if you receive financial aid to cover college costs, a less than 2.0 GPA can cost you your eligibility to continue to receive it. Luckily, this is a cumulative GPA rule. So if you managed to get a one point something GPA for one semester, the past semesters should be your saving grace. Of course, if you are a freshman in your first semester, a 2.0 or above GPA is a must. Reach out to and keep in touch with not only your financial aid office throughout the

These are my notes from Matrices and Vectors MATH 2333 at the University of Texas at Dallas from January 22, 2018. We learn a couple ways to prove a subspace is a subspace. A subspace of a vector space V is a subset in V, and is itself  a vector space that has underwent the operations of addition and scalar multiplication inherited from the original vector space V.  In other words the subspace must: 1. Include a zero vector 2. Be closed under addition (I f we add two elements of the subspace is the result in the subspace?) 3. Be closed under scalar multiplication (If we multiply elements in S by some scalar, is the result in S?) The elements and scalar mentioned will usually belong to all real numbers.  If any element in a set of vectors is restricted to all positive numbers or all negative numbers (can't be equal to 0) a zero vector is impossible. So always check for the first condition.  Lastly, all subsets can be