Given two
m × n
×
m
n
matrices AA and
BB, we define the sum to be the new
m × n
×
m
n
matrix
C = A + B
C
A
B
, where each entry,
c i , j
c
i
j
, is the sum of
a i , j
a
i
j
and
b i , j
b
i
j
.
(
a 1 , 1 a 1 , 2 ⋯ a 1 , n
a 2 , 1 a 2 , 2 ⋯ a 2 , n
⋮⋮⋮⋮
a m , 1 a m , 2 ⋯ a m , n
)+(
b 1 , 1 b 1 , 2 ⋯ b 1 , n
b 2 , 1 b 2 , 2 ⋯ b 2 , n
⋮ ⋮ ⋮ ⋮
b m , 1 b m , 2 ⋯ b m , n
)=(
a 1 , 1 + b 1 , 1 a 1 , 2 + b 1 , 2 ⋯ a 1 , n + b 1 , n
a 2 , 1 + b 2 , 1 a 2 , 2 + b 2 , 2 ⋯ a 2 , n + b 2 , n
⋮ ⋮ ⋮ ⋮
a m , 1 + b m , 1 a m , 2 + b m , 2 ⋯ a m , n + b m , n
)
a
1
1
a
1
2
⋯
a
1
n
a
2
1
a
2
2
⋯
a
2
n
⋮
⋮
⋮
⋮
a
m
1
a
m
2
⋯
a
m
n
b
1
1
b
1
2
⋯
b
1
n
b
2
1
b
2
2
⋯
b
2
n
⋮
⋮
⋮
⋮
b
m
1
b
m
2
⋯
b
m
n
a
1
1
b
1
1
a
1
2
b
1
2
⋯
a
1
n
b
1
n
a
2
1
b
2
1
a
2
2
b
2
2
⋯
a
2
n
b
2
n
⋮
⋮
⋮
⋮
a
m
1
b
m
1
a
m
2
b
m
2
⋯
a
m
n
b
m
n
(1)
(
-1 7 9
4 5 2
2 2 0
)+(
3 2 4
3 1 8
-1 5 -2
)=(
2 9 13
7 6 10
1 7 -2
)
-1 7 9
4 5 2
2 2 0
3 2 4
3 1 8
-1 5 -2
2 9 13
7 6 10
1 7 -2