Help with Hw assignmentMichael Chiu
Math3CA1M12Jaramillo
WeBWorK assignment number HW
10 is due : 08/04/2012 at 11:59pm PDT.
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1.
(1 pt)
Does the following set of vectors constitute a vector space?
Assume ”standard” deFnitions of the operations.
The set of vectors in the Frst quadrant of the plane.
•
A. Yes
•
B. No
If not, which condition(s) below does it fail? (Check all that
apply)
•
A. Vector spaces must be closed under addition
•
B. Vector spaces must be closed under scalar multipli
cation
•
C. There must be a zero vector
•
D. Every vector must have an additive inverse
•
E. Addition must be associative
•
². Addition must be commutative
•
G. Scalar multiplication by 1 is the identity operation
•
H. The distributive property
•
I. Scalar multiplication must be associative
•
J. None of the above, it is a vector space
2.
(1 pt)
Does the following set of vectors constitute a vector space?
Assume ”standard” deFnitions of the operations.
The set of all polynomials of even degree.
•
A. Yes
•
B. No
If not, which condition(s) below does it fail? (Check all that
apply)
•
A. Vector spaces must be closed under addition
•
B. Vector spaces must be closed under scalar multipli
cation
•
C. There must be a zero vector
•
D. Every vector must have an additive inverse
•
E. Addition must be associative
•
². Addition must be commutative
•
G. Scalar multiplication by 1 is the identity operation
•
H. The distributive property
•
I. Scalar multiplication must be associative
•
J. None of the above, it is a vector space
3.
(1 pt)
Does the following set of vectors constitute a vector space?
Assume ”standard” deFnitions of the operations.
The set of all diagonal 2
?
2 matrices.
•
A. Yes
•
B. No
If not, which condition(s) below does it fail? (Check all that
apply)
•
A. Vector spaces must be closed under addition
•
B. Vector spaces must be closed under scalar multipli
cation
•
C. There must be a zero vector
•
D. Every vector must have an additive inverse
•
E. Addition must be associative
•
². Addition must be commutative
1
Answer