Linear Algebra Quiz
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VECTOR SPACES & SUBSPACES
Question 1
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Let
W
=
{
(
x
,
y
,
z
,
w
)
∈
R
4
:
x
+
2
y
−
z
=
0
and
2
x
+
4
y
−
2
z
+
w
=
0
}
W = \{(x, y, z, w) \in \mathbb{R}^4 : x + 2y - z = 0 \text{ and } 2x + 4y - 2z + w = 0\}
W
=
{(
x
,
y
,
z
,
w
)
∈
R
4
:
x
+
2
y
−
z
=
0
and
2
x
+
4
y
−
2
z
+
w
=
0
}
. Which of the following statements about
W
W
W
is correct?
A
W
W
W
is a subspace of
R
4
\mathbb{R}^4
R
4
with dimension 2, and the second constraint is redundant with the first
B
W
W
W
is a subspace of
R
4
\mathbb{R}^4
R
4
with dimension 3, and both constraints provide independent information
C
W
W
W
is not a subspace because the system of constraints is inconsistent for some values
D
W
W
W
is a subspace of
R
4
\mathbb{R}^4
R
4
with dimension 1, since both constraints must be satisfied simultaneously
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