Find the characteristic polynomial and the eigenvalues of the matrices in Exercises 1–8.
4.
Learn your wayIncludes step-by-step video
Chapter 5 Solutions
Linear Algebra and Its Applications (5th Edition)
Additional Math Textbook Solutions
Linear Algebra with Applications (2-Download)
College Algebra (7th Edition)
A Graphical Approach to College Algebra (6th Edition)
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
- In Exercises 19–20, solve the matrix equation for X. 1 -1 1 -1 5 7 8. 19. 2 3 0| X = 4 -3 1 1 3 5 -7 2 1 -arrow_forwardIn Exercises 5–8, use the definition of Ax to write the matrix equation as a vector equation, or vice versa. 5. 5 1 8 4 -2 -7 3 −5 5 -1 3 -2 = -8 - [18] 16arrow_forwardIn Exercises 11–16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.arrow_forward
- Please show step-by-step calculation for this matrix. If row operations are not required to find out eigenvectors, state why.arrow_forwardshow all the workarrow_forwardSuppose that A is a 3-by-3 real matrix with an eigenvalue of 2. If the characteristic polynomial of A is x³ - 4x²+x+6, what are the other eigenvalues? (a) -1 and 3 (b) 1 and -3 (c) -1 and -3 (d) 1 and 3arrow_forward
- For the characteristic polynomial of Matrix A, p(x) = x³ - 2x2 + x + 5, where xis the Eigen value of A, what is the value of det(A) ? OA. 5 B. -5 OC. -2 OD. 1arrow_forwardIn Exercises 8–19, calculate the determinant of the given matrix. Use Theorem 3 to state whether the matrix is singular or nonsingulararrow_forwardSection 5.1: 22 Let A be a square matrix and f (x) and arbitrary polynomial. Show that if A is an eigenvalue of A, then f(X) is an eigenvalue of f(A).arrow_forward
- Find the characteristic polynomial and the eigenvalues of the matrix. 11 9 9 11 The characteristic polynomial is (Type an expression using as the variable. Type an exact answer, using radicals as needed.)arrow_forwardA = [2 -1 |-2 3] let it be. a) Write the characteristic polynomial of the matrix A b)Find the eigenvalues and eigenspaces corresponding to this matrix. c) Is matrix A diagonalizable? Show me. d) A^8 =? (Guidance: Do not apply matrix multiplication. D = (P^-1)AP make use of)arrow_forwardSuppose A is a 2 × 2 matrix. Use the characteristic equation to show that A and AT have the same eigenvalues.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning