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Artyom0805 [142]
3 years ago
9

I BEG FOR HELP :(

Mathematics
1 answer:
Citrus2011 [14]3 years ago
5 0

Answer:

(3, 2)

Step-by-step explanation:

I will solve using the elimination method

 x + y = 5

- (x - y = 1)

---------------

       2y = 4

          y = 2

plug y = 2 into any equation and solve for x

x + 2 = 5

x = 3

(3, 2)

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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
N2-m: use m=7 and n=8 Please explain how to do this.
Ivenika [448]
If N = 8
if M = 7
then the equation is 8(2) - 7
do the multiplication first 8(2) = 16
now do the subtraction 16 - 7 = 9
8 0
3 years ago
Please help, I beg of y'all <br><br>FIND BD -
puteri [66]

9514 1404 393

Answer:

  14 units

Step-by-step explanation:

The angle bisector divides the sides proportionally.

  BD/BA = CD/CA

  (x+4)/8 = (2x+1)/12

  3(x +4) = 2(2x +1) . . . . . multiply by 24 (the least common denominator)

  3x +12 = 4x +2 . . . . . . . eliminate parentheses using the distributive property

  12 = x +2 . . . . . . . subtract 3x

  10 = x . . . . . . . . . subtract 2

Then the length of BD is ...

  BD = x +4

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  BD = 14

3 0
3 years ago
.(3x+1)(x-3)<br> Binomial
Dafna11 [192]

Answer:

3x^2−8x−3

Step-by-step explanation:

(3x+1)(x−3)

=(3x+1)(x+−3)

=(3x)(x)+(3x)(−3)+(1)(x)+(1)(−3)

=3x^2−9x+x−3

=3x^2−8x−3

5 0
3 years ago
If 2 (3t - 10) + t = 40 + 4t, what is the value of 3t?
Elenna [48]

Answer: 3t = 60

Step-by-step explanation:

3 0
3 years ago
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