(‑(4*x))+5, (‑(3*x))-5/9
Hannah went on a bike ride on Saturday and Sunday every weekend in November. She recorded the number of miles she rode each time
. The following line plot represents the number of miles she recorded. What is the difference between the longest and shortest number of miles?
1 answer:
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ANSWER
36√3 square units.
EXPLANATION
The area of a parallelogram is obtained by multiplying the base by the height.
We use the sine ratio to obtain the height.
The area becomes:
Answer:
(A) Set A is linearly independent and spans . Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors , we are to decide which of the given statements is true:
In Matrix , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans . Thus it is basis for
.