Recall from class that m is the vector space of all 2 x 2 matrices with real entries. let w be the set of all symmetric 2 x 2 matrices. (a) (5 points) show that w is a subspace of m2x2. (hint: the way lay does this, there are three things to check.) (b) (4 points) write down a basis for w. (hint: symmetric matrices look like c) (6 points) using the definition of basis, show that your basis really is a basis. (d) (1 point) fill in the blank with the correct number: the dimension of w is .