Question

Please Help !
Medal and fan!

Answer 1

\[\left[\begin{matrix}3 & 1 \\ 2 & 4\end{matrix}\right]\]
\[z=\frac{3}{5}\]

Calculate the A^n.Z

Answer 2

I will try

Answer 3

What's n? Z?

Answer 4

Z=3/5

Answer 5

n=?

Answer 6

Z is a column vector.

\[Z=\left(\begin{matrix}3 \\ 5\end{matrix}\right)\]

The line is a stray mark on he paper not a fraction. Try multiplying
Z by A once and compare the answer to Z. What happens?

Answer 7

A ^n multiple by Z

Answer 8

so how to find n

Answer 9

I know, humor me....

Answer 10

If YOU multiply AZ, what do you get?

Answer 11

Oops, make that if you multiply AZ, what do you get?

Answer 12

@fwizbang
Az=\[\left(\begin{matrix}14 \\ 26\end{matrix}\right)\]

Answer 13

@mathmale

Answer 14

Ok, now I see what's happening. We need to write Z as a linear combination of X and Y(which are eigenvectors of A.) So, find an a and a b such that Z=aX+bY

Answer 15

yes

Answer 16

Then if we now the eigenvalues, we can write the answer for a general integer n. If\[AX=\lambda _{x}X\] then \[A^nX=(\lambda _{x})^n X\]

Answer 17

Same idea for Y, so do yu know the eigenvalues for X and Y?

Answer 18

no

Answer 19

Ok. Multiply X by A and compare the answer to X. Same for Y.

Answer 20

It looks like you already did this on your sheet....

Answer 21

Multiply X by A
\[\left(\begin{matrix}2 \\ -2\end{matrix}\right)\]

Answer 22

How does that compare to X?

Answer 23

\[\left(\begin{matrix}2 \\ -2\end{matrix}\right)=\left(\begin{matrix}1 \\ -1\end{matrix}\right)\]

Answer 24

x 2 on the right? So the eigenvalue for X is 2.

Answer 25

Now do Y....

Answer 26

Thanks can you help one more Question

Answer 27

Sure. What do you got?

Answer 28

-2y^2=4x
Find the directrix and the focus of the parabola

Answer 29

@fwizbang

Answer 30

So if you can write the equation as

\[(y-k)^2=4p(x-h)\]

then the focus it at (h+p,k) and the directrix is x=h-p.( I just googled parabola)

Answer 31

-2y^2=4x
divided -2 on both sides

y^2=-2x
so then

Answer 32

So 4p=-2, p=?
PS (y-0)^2=y^2.

Answer 33

p=-1/2
focus is(-1/2,0)
Right

Answer 34

yes!

Answer 35

Directis=-1/2

Answer 36

Careful h minus p.....

Answer 37

0-(-1/2)=1/2

so that directix =1/2

Answer 38

Now you got it.

Answer 39

yes thanks :) @fwizbang