MAS 2103 Final: MAS 2103 FAU Final10
Document Summary
Directions: make sure to show all necessary work to receive full credit. If you need extra space please use the back of the sheet with appropriate labeling. (1) state the following de nitions. A is an n n-matrix and f. (make sure to include the correct quanti ers. ) (a) the scalar is an eigenvalue of a if (b) the eigenspace corresponding to is. Is this set a linearly (3) determine whether the following system of equations is consistent or not. If it is consistent give the general solution. 2x1 +3x2 +2x3 +x4 = 5 x3 (4) let. Use co-factor expansion to determine the determinant of a. Only use your cal- culator to check your answer. 0 3 0 4 (5) consider the function t : r2 r3 de ned by. T (x, y) = (2x 3y, 4x, x + y): prove that t is a linear transformation. 3: find at the standard matrix representation of s. then nd rref(at ).
