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 .
Answer:
2.3
Step-by-step explanation:
138 divided by 60=2.3
divide the amount consumed by the total number of households involved
Answer:
x = 12
Step-by-step explanation:
The diagram shows an equilateral triangle (because all angles are congruent). All sides in equilateral triangle are congruent, so
Solve the equation
Check this value:
Thus,
This is hard in mathematical language, but there is only this way to present it. Let us denote by A the consentration of the substance and by A' its rate.
We have that b/A= t+c where c is a constant.
Hence A=b/(c+t)
By differentiating, we get that A'=-b/(C+t)^2
Then, we have that -(A)^2=A'/b
Hence at any point, we have that if we make the concentration 17 times, we have that there is a 17 times bigger , the rate will become bigger by 17*17, hence 289 times faster.
It would be 384.58, or 384.57909