Which correctly gives the location of the point (–19, 0)?

Mathematics

2 answers:

mafiozo [28]3 years ago

8 0

(-19,0) is located on the x-axis

xxTIMURxx [149]3 years ago

6 0

<span>A. x-axis</span>
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River C is 100 miles longer than River D. If the sum of their lengths is 5,570 miles, what is the length of each river?

lyudmila [28]

Let the Length of River D be : P

Given : River C is 100 Miles Longer than River D

⇒ Length of River C = P + 100

Given : The Sum of Both Rivers is 5570 Miles

⇒ P + (P + 100) = 5570

⇒ 2P + 100 = 5570

⇒ 2P = 5570 - 100

⇒ 2P = 5470

⇒ P = 2735

⇒ Length of River D is : 2735 Miles

⇒ Length of River C is : (P + 100) = (2735 + 100) = 2835 Miles

7 0

4 years ago

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:

$det(A-λI)=0$