Find the eigenvalues and eigenvectors of the following matrices. a. _ 1 5 2 4 b. _ 0 1 1

QUESTION:

Find the eigenvalues and eigenvectors of the following matrices.

a. \(\left[\begin{array}{ll} 1 & 5 \\ 2 & 4 \end{array}\right]\)

b. \(\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]\)

c. \(\left[\begin{array}{rr} 10 & -6 \\ 18 & -11 \end{array}\right]\)

d. \(\left[\begin{array}{rr} 0 & 1 \\ -1 & 0 \end{array}\right]\)

e. \(\left[\begin{array}{ll} 1 & 3 \\ 3 & 1 \end{array}\right]\)

f. \(\left[\begin{array}{rr} 1 & 1 \\ -1 & 3 \end{array}\right]\)

g. \(\left[\begin{array}{rrr} -1 & 1 & 2 \\ 1 & 2 & 1 \\ 2 & 1 & -1 \end{array}\right]\)

h. \(\left[\begin{array}{rrr} 1 & 0 & 0 \\ -2 & 1 & 2 \\ -2 & 0 & 3 \end{array}\right]\)

i. \(\left[\begin{array}{rrr} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 0 & -2 & 3 \end{array}\right]\)

j. \(\left[\begin{array}{lll} 2 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{array}\right]\)

k. \(\left[\begin{array}{rrr} 1 & -2 & 2 \\ -1 & 0 & -1 \\ 0 & 2 & -1 \end{array}\right]\)

l. \(\left[\begin{array}{lll} 3 & 1 & 0 \\ 0 & 1 & 2 \\ 0 & 1 & 2 \end{array}\right]\)

m. \(\left[\begin{array}{rrr} 1 & -1 & 4 \\ 3 & 2 & -1 \\ 2 & 1 & -1 \end{array}\right]\)

n. \(\left[\begin{array}{rrr} 1 & -6 & 4 \\ -2 & -4 & 5 \\ -2 & -6 & 7 \end{array}\right]\)

o. \(\left[\begin{array}{rrr} 3 & 2 & -2 \\ 2 & 2 & -1 \\ 2 & 1 & 0 \end{array}\right]\)

p. \(\left[\begin{array}{llll} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end{array}\right]\)