Math 3013
Homework Set 6
Problems from
§
3.1 (pgs. 134136 of text): 11,16,18
Problems from
§
3.2 (pgs. 140141 of text): 4,8,12,23,25,26
1.
(Problems 3.1.11 and 3.1.16 in text). Determine whether the given set is closed under the usual
operations of addition and scalar multiplication, and is a (real) vector space.
(a) The set of all diagonal
n
×
n
matrices.
(b) The set
P
n
of all polynomials in
x
, with real coeﬃcients and of degree less than or equal to
n
, together
with the zero polynomial.
2. (Problem 3.1.18 in text). Determine whether the following statements are true or false.
(a) Matrix multiplication is a vector space operation on the set
M
m
×
n
of
m
×
n
matrices.
(b) Matrix multiplication is a vector space operation on the set
M
n
×
n
of square
n
×
n
matrices.
(c) Multiplication of any vector by the zero scalar always yields the zero vector.
(d) Multiplication of a nonzero vector by a nonzero scalar always yields a nonzero vector.
(e) No vector is its own additive inverse.
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 Spring '08
 BINEGAR
 Math, Algebra, Vector Space

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