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Kunze Linear Algebra
· Problem 3.5.7
Linear Transformations
Mathematics — Methods · annihilator-of-subspace
Problem
Let
α
1
=
(
1
,
0
,
−
1
,
2
)
\alpha_1 = (1, 0, -1, 2)
α
1
=
(
1
,
0
,
−
1
,
2
)
and
α
2
=
(
2
,
3
,
1
,
1
)
\alpha_2 = (2, 3, 1, 1)
α
2
=
(
2
,
3
,
1
,
1
)
, and let
W
W
W
be the subspace of
R
4
R^4
R
4
spanned by
α
1
\alpha_1
α
1
and
α
2
\alpha_2
α
2
. Which linear functionals
f
f
f
:
f
(
x
1
,
x
2
,
x
3
,
x
4
)
=
c
1
x
1
+
c
2
x
2
+
c
3
x
3
+
c
4
x
4
f(x_1, x_2, x_3, x_4) = c_1 x_1 + c_2 x_2 + c_3 x_3 + c_4 x_4
f
(
x
1
,
x
2
,
x
3
,
x
4
)
=
c
1
x
1
+
c
2
x
2
+
c
3
x
3
+
c
4
x
4
are in the annihilator of
W
W
W
?
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