Show that the determinant of the matrix B = xl – A, where I is an identity matrix and A = [1 2 01 4|, ís the polynomial x3 – 8x2 + x – 6. Moreover, show that A satisfies this [4 2 6] polynomial, that is, A3 – 8A? + A – 61 = 0. Use this fact to show that the inverse of A can be expressed as A-1 = (A² – 8A + I). This follows from the Cayley-Hamilton theorem. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Show that the determinant of the matrix B = xl – A, where I is an identity matrix and A =
[1 2 01
4|, ís the polynomial x3 – 8x2 + x – 6. Moreover, show that A satisfies this
[4 2 6]
polynomial, that is, A3 – 8A? + A – 61 = 0. Use this fact to show that the inverse of A can
be expressed as A-1 = (A² – 8A + I). This follows from the Cayley-Hamilton theorem.
%3D
Transcribed Image Text:Show that the determinant of the matrix B = xl – A, where I is an identity matrix and A = [1 2 01 4|, ís the polynomial x3 – 8x2 + x – 6. Moreover, show that A satisfies this [4 2 6] polynomial, that is, A3 – 8A? + A – 61 = 0. Use this fact to show that the inverse of A can be expressed as A-1 = (A² – 8A + I). This follows from the Cayley-Hamilton theorem. %3D
Expert Solution
steps

Step by step

Solved in 2 steps with 4 images

Blurred answer
Knowledge Booster
Determinant
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,