Question

Using diagonalization, find A^n if n is a positive integer and A = MATRIX below :^)

Answer 1

\[\left[\begin{matrix}3& -1&0 \\ -1 & 2&-1\\ 0& -1 & 3\end{matrix}\right]\]

Answer 2

start by finding eigenvalues and eigenvectors

Answer 3

My professor has been spoon feeding us throughout the semester. Is it important that I know how to find the eigenvalue and vector by hand. I am currently using MatLab a program he instructed us to use.

Answer 4

Eigenvalue with Eigentvector
3 [1,0,-1];
4 [1,-1,1];
1 [1,2,1];

Answer 5

matlab is fine but it is good to know how to work these manually

Answer 6

split the given matrix \(A\) like this : \[A=S\Lambda S^{-1}\]

where \(S=\) eigenvector matrix
\(\Lambda\) = diagonal matrix whose diagonal elements are eigenvalues

Answer 7

I don't know if my professor is just being lazy, but he is also a student, kind of working his way up and he teachers the class. He told me and number of other students in particular majors, such as computer science or engineering for example that not much of this will be needed in our majors.

Answer 8

but still an understanding of the concepts are important. sort to speak.

Answer 9

Yes matlab makes more sense when we know how it is working in the background

this lecture covers everything about diagonalization
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-22-diagonalization-and-powers-of-a/

Answer 10

give it to me straight doc, is my professor hoodwinking students out of an education?