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.
Answer:
84 cubic feet
Step-by-step explanation:
First, multiply the numbers to get the volume.
5 2/5 * 4 2/3= 25 1/5
25 1/5 * 4 4/9= 112
Then, we can find 3/4 of that.
112*3/4=84.
Answer:
9.2
Step-by-step explanation:
Answer:
A. Correct choice is C
B. Correct choice is B
Step-by-step explanation:
4 times the number x is 4x.
The sum of 4 times the number x and 26 is 4x+26.
The sum of 4 times the number x and 26 is 130, then
4x+26=130.
Correct option is option C.
Solve this equation:
4x=130-26,
4x=104,
x=26.
A I think but I’m not postitive
