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Problem
Problem
If
A
=
[
1
0
1
/
2
1
]
A = \begin{bmatrix} 1 & 0 \\ 1/2 & 1 \end{bmatrix}
A
=
[
1
1/2
0
1
]
, then
A
100
A^{100}
A
100
is equal to a.
[
1
0
25
0
]
\begin{bmatrix} 1 & 0 \\ 25 & 0 \end{bmatrix}
[
1
25
0
0
]
b.
[
1
0
50
1
]
\begin{bmatrix} 1 & 0 \\ 50 & 1 \end{bmatrix}
[
1
50
0
1
]
c.
[
1
0
(
1
/
2
)
100
1
]
\begin{bmatrix} 1 & 0 \\ (1/2)^{100} & 1 \end{bmatrix}
[
1
(
1/2
)
100
0
1
]
d. None of these
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