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 .
It is convenient to let a spreadsheet or graphing calculator do the math for this. Functions can be defined for cost and profit, and evaluated at each of the volumes of interest.
a1) For 200 cars, the Outside location yields the greatest profit
a2) For 300 cars, the City location yields the greatest profit
b) The sites yield the same profit for a volume of 278 cars.
Answer:
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
Step-by-step explanation:
Volume=576π cubic centimeters
Radius=8 cm
h=?
Her work:
Volume of a cyclinder=πr^2h
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h=9π cm
Correct workings:
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h= 9 centimeters
Her error is in step 4
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
You have to use the formula a=principal or initial amount(1+rate or %)^time or years
Answer:
=9 * 1000 / 3600
=9000 / 3600
=2.5m/s
note that 1000m makes 1km and 3600seconds make an hour
Step-by-step explanation: