MATH 551 Midterm: MATH 551 KSU Test F6 u05

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

Document Summary

Then a2[3, 4]t = c[1, 2]t for some scalar c. (3) suppose that a is a 3 3 matrix with 2 and 3 as its only eigenvalues. Then a is de cient. (4) the only non-de cient 3 3 matrix that has 1 as its only eigenvalue is the identity matrix. (5) suppose that the characteristic polynomial of a is p( ) = 3( 2)( + 3)2. Then, the nullspace of a can be at most 2 dimensional. Then a must be a 4 4 matrix. (6) suppose that a has characteristic polynomial p( ) = ( 2)2( 3)( 4). Then det(a) = 24. (7) suppose that a is diagonalizable over r. then the eigenvalues of a2 are all positive. (8) it is possible for the = 2 eigenspace of a matrix to contain only one non-zero vector. Then the matrix b below would have at least one non-real entry. (cid:20)