NEED HELP!!! I DON"T UNDERSTAND HOW TO FILL THIS IN. WILL MARK BRAINLIEST FOR THE BEST ANSWER!!!
1 answer:
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Answer:
a) True
b) False
c) False
d) False
e) True
Step-by-step explanation:
a) Each basis of V has four vectors. Then any set of 5 vectors must be linear dependent (LD).
b) Suppose that is a basis of V. Considere the set
where
are scalars. The set has 5 vectors but
because
is not belong to A and
is linear independent of
c) Suppose that is a basis of V. Considere the set
where
are scalars. A has four nonzero vectors but isn't a basis because is a LD set.
d) Suppose that is a basis of V. Considere the set
where
are scalars. A has 3 nonzero vectors but isn't a basis because is a LD set.
e) Since any basis of V must have 4 elements, then a set of three vectors cannot generate V.