Exercise 8.5.4. Take the 2 x 2 matrix A = ³) and consider the matrix A-X. I where A is a variable scalar and I is 3 the identity matrix. Compute det(A - XI). Using the 2 x 2 formula. Solve for A when setting this determinant equal to zero. Now for each solution solve the equation Ax = Ax for x. You have just found your first eigen-pair!
Exercise 8.5.4. Take the 2 x 2 matrix A = ³) and consider the matrix A-X. I where A is a variable scalar and I is 3 the identity matrix. Compute det(A - XI). Using the 2 x 2 formula. Solve for A when setting this determinant equal to zero. Now for each solution solve the equation Ax = Ax for x. You have just found your first eigen-pair!
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.2: Multiplicative Inverses
Problem 41PS
Related questions
Question
![Exercise 8.5.6. Try the same process from Exercise 8.5.4 for a 3 × 3 matrix of your choosing. What goes wrong if you try
to find the determinant using the pivot method? Which method is actually more computable from your perspective in this
situation? Why does all of this help you understand why the first time I tried to teach linear algebra using only one method
for determinants I was rather foolish?
(13²)
and consider the matrix A-X. I where A is a variable scalar and I is
the identity matrix. Compute det(A - X. I). Using the 2 × 2 formula. Solve for λ when setting this determinant equal to
zero. Now for each solution solve the equation Ax = Xx for x. You have just found your first eigen-pair!
Exercise 8.5.4. Take the 2 × 2 matrix A =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80d412e1-3977-44a4-94cf-90c8aaabb7a1%2F6ecd2912-cb74-4f52-b128-d24f443f0688%2Fs1zetpn_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 8.5.6. Try the same process from Exercise 8.5.4 for a 3 × 3 matrix of your choosing. What goes wrong if you try
to find the determinant using the pivot method? Which method is actually more computable from your perspective in this
situation? Why does all of this help you understand why the first time I tried to teach linear algebra using only one method
for determinants I was rather foolish?
(13²)
and consider the matrix A-X. I where A is a variable scalar and I is
the identity matrix. Compute det(A - X. I). Using the 2 × 2 formula. Solve for λ when setting this determinant equal to
zero. Now for each solution solve the equation Ax = Xx for x. You have just found your first eigen-pair!
Exercise 8.5.4. Take the 2 × 2 matrix A =
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