Question

Let A be a 2 x 2 such that [2] is an eigenvector for
[3]
A with eigenvalue 1, and [1] is an eigenvector for A
[2]
with eigenvalue 1/2. If v = [-1]
[1 ]

Compute A^4 V?

Help please.

Answer 1

Is this calculus

Answer 2

linear algebra

Answer 3

Oh so Algebra 2

Answer 4

I sctuslly want to learn how this works im in Geometry so learning ahead can't be that bad

Answer 5

(I just did some research myself from wikipedia so i may not be reliable)
Maybe let the matrix be \(\left(\begin{matrix}a&b\\c&d\end{matrix}\right)\)?

Answer 6

Whats a matrix

Answer 7

I thought you learnt what's a matrix...
Well before you learn eigenvalues and eigenvectors you must learn matrix right?

Answer 8

so i have to find A using the eigenvectors and eigenvalues?

Answer 9

Im only 10th grade

Answer 10

but I thought you are learning ahead?

P.S. no bragging by I knew matrix since i was in 5th grade or so

Answer 11

but*

Answer 12

hope that helps

Answer 13

https://www.google.com.hk/search?q=khanacademy+matrix&oq=khanacademy+matrix&aqs=chrome..69i57j0l5.12342j0j7&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8

Answer 14

@kc_kennylau Im happy for you but Im in tenth grade know what vectors are

Answer 15

Eigenvector is not exactly related to vector :)

Answer 16

How do i know i should find [P^-1] and D^4?

Answer 17

I was bragging that i knew what vectors are lol im studying on Khan Academy

Answer 18

wait @jlg030597 I thought you were the question owner lol fml

Answer 19

@jan4712 but there ain't P and D...

Answer 20

Nope Jan is I wanted to learn how it worked

Answer 21

@jan4712 if you didn't know, now, you know. That's the process to find out exponential matrix

Answer 22

sorry i was referring to loser66. so D^n for A^n?

Answer 23

\[A^n \neq D^n\]
\[A^n = P^- * D^n*P\] 3 matrices time together, and the order MUST be that.

Answer 24

Oh my Im so confused now

Answer 25

@jlg030597 you have to have some basis to solve this problem

Answer 26

i get it. thank you!

Answer 27

np