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Mathematics
Mathematics
Problem
Let
A
=
[
1
a
a
0
1
b
0
0
1
]
A = \begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1 \end{bmatrix}
A
=
1
0
0
a
1
0
a
b
1
,
a
,
b
∈
R
a, b \in \mathbb{R}
a
,
b
∈
R
. If for some
n
∈
N
n \in \mathbb{N}
n
∈
N
.
A
n
=
[
1
48
2160
0
1
96
0
0
1
]
A^n = \begin{bmatrix} 1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1 \end{bmatrix}
A
n
=
1
0
0
48
1
0
2160
96
1
then
n
+
a
+
b
n + a + b
n
+
a
+
b
is equal to ______ [NA July 25, 2022 (II)]
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