Math 240 fall 2011 exam 2. *** there are questions on both sides of this paper *** Answer each question on a separate sheet of paper. On each sheet, put your name, your section leader"s name and your section meeting time. You must be careful on arithmetic check. No proof is needed for true-false questions; just write clearly. You may assume given matrix expressions are well de ned (i. e. the matrix sizes are compatible): (15 points) below are a matrix a and the matrix rref(a) produced by matlab. Write down a basis for each of the following (no justi cation required). (a) (5 pts. ) Row(a), the row space of a. (b) (5 pts. ) Col(a), the column space of a. (c) (5 pts. ) Nul(a), the null space of a: (10 points) in r2, the vertices of a triangle t are (cid:18)4. What is the area of t : (10 points) compute the determinant of the matrix.
