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Unformatted text preview: ALSE. The null space of A is a subspace of R3 while the the null space of
AT is a subspace of R2 . It is meaningless to speak of them being perpendicular.
b) TRUE. We show they are independent. Then their span is a three dimensional subspace
of R3 which is necessarily all of R3 . Suppose c11 + c22 +3 3 = Dotting with 1 we get
v
v
v
0.
v
c1 = 0. Similarly, dotting with 2 and 3 gives c2 = 0 and c3 = 0.
v
v
c) TRUE. Take any basis and apply GramSchmidt.
d) TRUE. The 3 × 3 matrix T has rank at most the rank of the 3 × 1 matrix which is
uv
u
T
at most 1. Thus is not inve...
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 Fall '05
 HUI
 Linear Algebra, Algebra, Vectors

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