Linear Algebra Quiz
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EIGENVALUES & EIGENVECTORS
Question 1
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Let
A
=
(
1
0
−
2
3
)
A = \begin{pmatrix} 1 & 0 \\ -2 & 3 \end{pmatrix}
A
=
(
1
−
2
0
3
)
. To compute
A
k
A^k
A
k
, the matrix is diagonalized as
A
=
P
D
P
−
1
A = PDP^{-1}
A
=
P
D
P
−
1
. What are the diagonal entries of the matrix
D
k
D^k
D
k
?
A
1
k
1^k
1
k
and
3
k
3^k
3
k
B
1
k
1^k
1
k
and
(
−
2
)
k
(-2)^k
(
−
2
)
k
C
(
−
1
)
k
(-1)^k
(
−
1
)
k
and
3
k
3^k
3
k
D
(
−
1
)
k
(-1)^k
(
−
1
)
k
and
(
−
3
)
k
(-3)^k
(
−
3
)
k
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A
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