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Concept Questions: 10-07-2011
MA2940: Linear Algebra for Engineers
1)
If a subspace
S
is 7-dimensional in
R
9
, subspaces orthogonal to
S
can have what dimen-
sions?
2)
If
S
and
S
⊥
are orthogonal complements in space
U
, does
S
∪
S
⊥
=
U
?
3)
If
NS
(
A
) has dimension 4 and
RS
(
A
) =
C
(
A
T
) has dimension 6, do you have enough
information to ﬁnd the size of matrix
A
?
4)
A
T
y
=
d
is solvable when
d
is in which of the 4 subspaces? The solution
y
is unique
when which subspace contains only the zero vector?

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**Unformatted text preview: **5) Find the invertible submatrix (made of the pivot columns and rows) of the matrix -1 1 2 2-2-1 2 1 2-1 2-1 2 6) Decompose (3 , 2 , 1) T into v r + v n , where v r is in the row space and v n is in the null space of A = 2 1 4-1-2-4 3-12-12 TA: Kyle Wilson...

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