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Linear Independence
Linear Independence
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Foundation
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Question 1 of 4
120s
foundation (1/10)
state theorem
Vectors
v
1
,
…
,
v
k
∈
R
n
are LINEARLY INDEPENDENT when which condition holds?
Hide and think first
A.
The only solution to
∑
i
α
i
v
i
=
0
is the trivial one
α
1
=
⋯
=
α
k
=
0
.
B.
No
v
i
is a scalar multiple of any other
v
j
. (Pairwise non-collinear.)
C.
Each
v
i
is orthogonal to every other
v
j
—
⟨
v
i
,
v
j
⟩
=
0
for
i
=
j
.
D.
The vectors span
R
n
— every
x
∈
R
n
can be written as some
∑
i
α
i
v
i
.
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