Description
Exercises on eigenvalues and eigenvectors
Problem 21.1: (6.1 #19. Introduction to Linear Algebra: Strang) A three by
three matrix B is known to have eigenvalues 0, 1 and 2. This information
is enough to find three of these (give the answers where possible):
a) The rank of B
b) The determinant of BTB
c) The eigenvalues of BTB
d) The eigenvalues of (B2 + I)−1
Problem 21.2: (6.1 #29.) Find the eigenvalues of A, B, and C when
⎡ ⎤ ⎡ ⎤ ⎡ ⎤ 1 2 3 0 0 1 2 2 2
A = ⎣ 0 4 5 ⎦ , B = ⎣ 0 2 0 ⎦ and C = ⎣ 2 2 2 ⎦ .
0 0 6 3 0 0 2 2 2
1
18.06SC Linear Algebra
