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The Manga Guide to Linear Algebra by Ltd. Trend-Pro Co., Iroha Inoue, Shin Takahashi

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Dimension 155
R
m
is also a subspace of itself, as you might
have gueed from example 1.
A subspaces contain the zero factor,
which you could probably te from
lking at the example on page 152.
Remember, they must pa through the
origin!
0
0
0
x
2
x
3
1
1
O
x
1
Example 2
The x
1
x
2
-plane could also be a subspace of R
3
, and we could span it using the
vectors and , creating this set:
x
1
x
2
-plane
1
0
0
0
1
0
c
1
+ c
2
1
0
0
0
1
0
c
1
and c
2
are
arbitrary numbers
Example 2

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