Characteristic Equation, Eigenvalues and Eigenvector, In Exercise 15-28, find (a) the characteristic equation and (b) the eigenvalues (and corresponding eigenvectors) of the matrix.
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Elementary Linear Algebra (MindTap Course List)
- Determine a Sufficient Condition for Diagonalization In Exercises 23-26, find the eigenvalues of the matrix and determine there is a sufficient number of eigenvalues to guarantee that the matrix is diagonalizable by Theorem 7.6. [432011002]arrow_forwardCharacteristic Equation, Eigenvalues, and EigenvectorsIn Exercise 15-28, find a the characteristics equation and b the eigenvalues and corresponding eigenvectors of the matrix. [132121]arrow_forwardTrue or False? In Exercises 67 and 68, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a Geometrically, if is an eigenvalue of a matrix A and x is an eigenvector of A corresponding to , then multiplying x by A produce a vector x parallel to x. b If A is nn matrix with an eigenvalue , then the set of all eigenvectors of is a subspace of Rn.arrow_forward
- True or False? In Exercises 69 and 70, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a An eigenvalue of a matrix A is a scalar such that det(IA)=0. b An eigenvector may be the zero vector 0. c A matrix A is orthogonally diagonalizable when there exists an orthogonal matrix P such that P1AP=D is diagonal.arrow_forwardVerifying Eigenvalues and Eigenvectors in Exercises 1-6, verify that i is an eigenvalues of A and that Xi is a corresponding eigenvector. A=[223216120], 1=5,X1=(1,2,1)2=3,X2=(2,1,0)3=3,X3=(3,0,1)arrow_forwardVerifying Eigenvalues and EigenvectorsIn Exercises 1-6, verify that i is an eigenvalues of A and that Xi is a corresponding eigenvector. A=[4523], 1=1,X1=(1,1)2=2,X2=(5,2)arrow_forward
- Characteristic Equation, Eigenvalues and Eigenvectors In Exercise 15-28, find a the characteristic equation and b the eigenvalues and corresponding eigenvectors of the matrix. [223032012]arrow_forwardDetermining Eigenvectors In Exercise 9-12, determine whether X is an eigenvector of A. A=[31052] a X=(4,4) b X=(8,4) c X=(4,8) d X=(5,3)arrow_forwardCharacteristic Equation, Eigenvalues, and Basis In Exercises 1-6, find a the characteristic equation of A, b the eigenvalues of A, and c a basis for the eigenspace corresponding to each eigenvalue. A=[9432061411]arrow_forward
- True or False? In Exercises 67 and 68, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a The scalar is an eigenvalue of an nn matrix A when there exists a vector x such that Ax=x. b To find the eigenvalues of an nn matrix A. you can solve the characteristic equation det(IA)=0.arrow_forwardEigenvalues of Triangular and Diagonal Matrices In Exercises 41-44, find the eigenvalues of the triangular or diagonal matrix. [201034001]arrow_forwardDiagonalizing a Matrix In Exercise 7-14, find if possible a nonsingular matrix P such that P1AP is diagonal. Verify that P1AP is a diagonal matrix with the eigenvalues on the main diagonal A=[122252663] See Exercise 23, section 7.1. Characteristic Equation, Eigenvalues, and EigenvectorsIn Exercise 15-28, find a the characteristics equation and b the eigenvalues and corresponding eigenvectors of the matrix. [122252663]arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage