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denpristay [2]
3 years ago
5

Mr. and Mrs. Preston and their two children are very excited about their upcoming

Mathematics
1 answer:
ki77a [65]3 years ago
7 0

Answer:

They will spend less at the sunny side hotel

Step-by-step explanation:

The attachment completes the question.

From the question, we understand that there are 4 individuals involved.

  • Mr. Preston (1)
  • Mrs. Preston (1)
  • The children (2)

And they will spend one night

First, we need to calculate the expenses in Traveler's hotel.

Rate = \$107.10 (for 3 people)

Additional\ Person = \$21.55 (for 1 person)

Breakfast = \$8.75 * 4 (for 4 people)

Tax = \$16.85

Total Expenses

Total = \$107.10 + \$21.55 + \$8.75* 4 + \$16.85

Total = \$107.10 + \$21.55 + \$35.00 + \$16.85

Total = \$108.50

For Sunny Side hotel:

Rate = \$152.95 (for 4 people)

Tax = \$21.34

Total Expenses:

Total = \$152.95 + \$21.34

Total = \$174.29

By comparison, they will spend less at the sunny side hotel.

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Step-by-step explanation:

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Suppose that v is an eigenvector of matrix A with eigenvalue λA, and it is also an eigenvector of matrix B with eigenvalue λB. (
galben [10]

Answer:

(a) Yes, λ_{A}+λ_{B}

(b) Yes, λ_{A}λ_{B}

Step-by-step explanation:

First, lets understand what are eigenvectors and eigenvalues?

Note: I am using the notation λ_{A} to denote Lambda(A) sign.

v is an eigenvector of matrix A with eigenvalue λ_{A}

v is also eigenvector of matrix B with eigenvalue λ_{B}

So we can write this in equation form as

Av=λ_{A}v

So what does this equation say?

When you multiply any vector by A they do change their direction. any vector  that is in the same direction as of Av, then this v  is called the eigenvector of A. Av is λ_{A} times the original v. The number λ_{A} is the eigenvalue of A.

λ_{A} this number is very important and tells us what is happening when we multiply Av. Is it shrinking or expanding or reversed or something else?

It tells us everything we need to know!

Bonus:

By the way you can find out the eigenvalue of Av by using the following equation:

det(A-λI)=0

where I is identity matrix of the size of same as A.

Now lets come to the solution!

(a) Show that v is an eigenvector of A + B and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(A+B)(v)=Av+Bv=(λ_{A})v + (λ_{B})v=(λ_{A}+λ_{B})(v)

so,  (A+B)(v)=(λ_{A}+λ_{B})(v)

which means that v is also an eigenvector of A+B and the associated eigenvalues are λ_{A}+λ_{B}

(b) Show that v is an eigenvector of AB and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(AB)(v)=A(Bv)=A(λ_{B})=λ_{B}(Av)=λ_{B}λ_{A}(v)=λ_{A}λ_{B}(v)

so,  

(AB)(v)=λ_{A}λ_{B}(v)

which means that v is also an eigenvector of AB and the associated eigenvalues are λ_{A}λ_{B}

5 0
3 years ago
Pls help extra points and mark brainlist
Zanzabum

Answer:

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Step-by-step explanation:

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MatroZZZ [7]
Hi there!

The correct answer is Rational Number.

\bf{EXPLANATION} :-

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~ Hope it helps!
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