MATH 240 Final: MATH240 MATH232 Fall2007 Final for MATH240 Solution

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 240
• Professor: All

Document Summary

No credit will be given for just writing down the answer: if the answer space provided is not su cient, write your answer on the back of the previous page. Clearly mark the question number: good luck. Final, math 232, fall 2007: let a be the matrix. 0 1 3 (a) (6 points) compute the characteristic polynomial of a. Your nal answer should be of the form ax3 + bx2 + cx + d. (b) (2 points) use part a. to decide whether a is invertible or not. We compute the determinant of the matrix a xi: Solution: analyzing each intersection, we obtain the equations x1 + x2 = 80, x1 + x3 = 30, and x2 x3 x4 = 0. Row 2 gives x2 = 50 + x3. Row 1 gives x1 = 30 x3. Since x1 cannot be negative, we see that x3 30. Thus the maximum possible value of x3 is 30.