Answer:
a) False
b) False
c) True
d) False
e) False
Step-by-step explanation:
a. A single vector by itself is linearly dependent. False
If v = 0 then the only scalar c such that cv = 0 is c = 0. Hence, 1vl is linearly independent. A set consisting of a single vector v is linearly dependent if and only if v = 0. Therefore, only a single zero vector is linearly dependent, while any set consisting of a single nonzero vector is linearly independent.
b. If H= Span{b1,....bp}, then {b1,...bp} is a basis for H. False
A sets forms a basis for vector space, only if it is linearly independent and spans the space. The fact that it is a spanning set alone is not sufficient enough to form a basis.
c. The columns of an invertible n × n matrix form a basis for Rⁿ. True
If a matrix is invertible, then its columns are linearly independent and every row has a pivot element. The columns, can therefore, form a basis for Rⁿ.
d. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. False
Row operations can not affect linear dependence among the columns of a matrix.
e. A basis is a spanning set that is as large as possible. False
A basis is not a large spanning set. A basis is the smallest spanning set.
The answer is 35 because 20-10=10 then 25+10=35 so niki made 35 points on her final round
You paid 15 cent because 3 divided by 20 is 0.15
Answer:
confusion?
Step-by-step explanation:
your welcome
Answer:
Hey buddy whatsup? All good
Coming to the question fig 1 and 3 aren't functions
Coz.... Reason for fig 1... Every distinct element of domain must have a unique element in codomain, but in this fig the same element has more than two unique elements which is a relation not a function.
Reason for fig 3 every element in domain must have an unique element in codomain but in this fig the element c doesn't have any unique element hence it isn't a function.....
Thank you
