MATH 551 Midterm: Kansas State MATH 551 551TF5 f04

• School: Kansas State University
• Department: Mathematics
• Course: MATH 551
• Professor: All

Document Summary

5. 1 (1) the following matrices have the same determinant. 2 2 18 22 (2) let a be a 3 3 matrix. Then det(5a) = 5 det(a). (3) let a and b be 3 3 matrices. Then det(a + b) = det(a) + det(b). (4) 3 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (5) the following matrices have the same determinant. 0 (6) the following matrices have the same determinant. 1 2 1 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (2) the following matrices have the same determinant. 1 2 1 (3) the following numbers are equal. (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) 2 (4) the following matrices have the same determinant. 3 1 5 (5) for all n n matrices a and b, det(ab) = (det ba). (6) suppose that det a = 2, det(a + i) = 3 and det(a + 2i) = 5. 5. 3 (1) in the following system, you may assume that the determinant of the coef cient matrix is not zero. 2x + 3y 5z + 3w = 5.