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Mathematics
Mathematics
Problem
If
A
=
[
1
1
1
0
1
1
0
0
1
]
A = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}
A
=
1
0
0
1
1
0
1
1
1
and
M
=
A
+
A
2
+
A
3
+
⋯
+
A
20
M = A + A^2 + A^3 + \dots + A^{20}
M
=
A
+
A
2
+
A
3
+
⋯
+
A
20
, then the sum of all the elements of the matrix
M
M
M
is equal to ________.
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