?Computer Lab: Eigenvectors For each matrix (a)-(h), find the eigenvalues and

Chapter 5, Problem 79

(choose chapter or problem)

Computer Lab: Eigenvectors For each matrix (a)-(h), find the eigenvalues and eigenvectors. To make quick work of this, use computer software (e.g., IDE, Derive, Matlab, or other computer algebra systems). From your results, list conjectures (and illustrations) of what you might be able to predict for eigenvalues and eigenvectors from just looking at a 2 ⨉ 2 matrix (without calculations).

(a) \(\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]\)

(b) \(\left[\begin{array}{ll} 2 & 0 \\ 0 & 2 \end{array}\right]\)

(c) \(\left[\begin{array}{ll} 2 & 1 \\ 0 & 2 \end{array}\right]\)

(d) \(\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]\)

(e) \(\left[\begin{array}{ll} 1 & 4 \\ 1 & 1 \end{array}\right]\)

(f) \(\left[\begin{array}{ll} 2 & 1 \\ 1 & 2 \end{array}\right]\)

(g) \(\left[\begin{array}{ll} 0 & 0 \\ 0 & 1 \end{array}\right]\)

(h) \(\left[\begin{array}{ll} 1 & 0 \\ 0 & 0 \end{array}\right]\)

Equation Transcription:

Text Transcription:

[1  0 _ 0  1]

[2  0 _ 0  2]

[2  1 _ 0  2]

[1  1 _ 1  1]

[1  4 _ 1  1]

[2  1 _ -1  2]

[0  0 _ 0  1]

[1  0 _ 0  0]