Concept explainers
Exercises 19–23 concern the polynomial
p(t) = a0 + a1t + … + an−1tn−1 + tn
and an n × n matrix Cp called the companion matrix of p:
Cp =
20. Let p(t) = (t − 2)(t − 3)(t − 4) = −24 + 26t − 9t2 + t3 Write the companion matrix for p(t), and use techniques from Chapter 3 to find its characteristic polynomial.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Linear Algebra and Its Applications (5th Edition)
Additional Math Textbook Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Algebra 1
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
- Suppose A is a 2 x 2 matrix such that A and 1 A What is A-1?arrow_forwardCompute the determinants in Exercises 9–14 by cofactor expansions. At each step, choose a row or column that involves the least amount of computation.arrow_forwardQuestion 1 Set up the relevant matrices and determine the definiteness of the following quadratic forms: 1.1 Q(x1, x2) = xỉ + 2x1x2 – 8x, subject to x1 + x2 = 0. 1.2 Q(11, x2, 23, X4, 13) = 2x² + 4x3 + až + 3xž.arrow_forward
- Exercise 5H. Let X be a square matrix with real entries such that XTX = I. Argue that det(X) = +1.arrow_forwardLet - (; ;) 5 3 A = 2 1 a) Calculate A-1 by any method. b) Using your answer to part (a), explicitly compute a matrix X so that -1 XA= B:= 1 -8 3 ||arrow_forwardShow that the matrix X -1 X : 0 0 X is Positive Definite if x > √n-1. The lower right block is x In-1 · Hint: Use (A is SPD ⇒ det(A;) > 0 ; for all principal sub-matrices )arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning