Answer the following questions and, in each case, give geometric explanations of your answers: (a) Is it possible to have a pair of one−dimensional subspaces U 1 and U 2 of ℝ 3 such that U 1 ∩ U 2 = { 0 } ? (b) Is it possible to have a pair of two−dimensional subspaces V 1 and V 2 of ℝ 3 such that V 1 ∩ V 2 = { 0 } ?
Answer the following questions and, in each case, give geometric explanations of your answers: (a) Is it possible to have a pair of one−dimensional subspaces U 1 and U 2 of ℝ 3 such that U 1 ∩ U 2 = { 0 } ? (b) Is it possible to have a pair of two−dimensional subspaces V 1 and V 2 of ℝ 3 such that V 1 ∩ V 2 = { 0 } ?
Solution Summary: The author explains that it is possible to have a pair of one-dimensional subspaces U_1 and
Answer the following questions and, in each case, give geometric explanations of your answers: (a) Is it possible to have a pair of one−dimensional subspaces
U
1
and
U
2
of
ℝ
3
such that
U
1
∩
U
2
=
{
0
}
? (b) Is it possible to have a pair of two−dimensional subspaces
V
1
and
V
2
of
ℝ
3
such that
V
1
∩
V
2
=
{
0
}
?
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