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Suppose that A is an n x n matrix satisfying A² = In. Let P = ½ (I₂ − A) 1 Mark only correct statements. O a. The only possible eigenvalues of A are 1 and -1. b. The generalized eigenspaces of the matri A equal to the corresponding eigenspaces of A. c. The null space of P is the eigenspace of A corresponding to the eigenvalue −1. Od. The matrix A may not be diagonalizable. Oe. The null space of P is the eigenspace of A corresponding to the eigenvalue 1.

Suppose that A is an n x n matrix satisfying A² = In. Let P = ½ (I₂ − A) 1 Mark only correct statements. O a. The only possible eigenvalues of A are 1 and -1. b. The generalized eigenspaces of the matri A equal to the corresponding eigenspaces of A. c. The null space of P is the eigenspace of A corresponding to the eigenvalue −1. Od. The matrix A may not be diagonalizable. Oe. The null space of P is the eigenspace of A corresponding to the eigenvalue 1.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 24EQ
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Suppose that A is an n x n matrix satisfying A² = In. Let P = ½-½(L, − A) - Mark only correct statements. a. The only possible eigenvalues of A are 1 and -1. b. The generalized eigenspaces of the matri A equal to the corresponding eigenspaces of A. O c. The null space of P is the eigenspace of A corresponding to the eigenvalue - 1. Od. The matrix A may not be diagonalizable. The null space of P is the eigenspace of A corresponding to the eigenvalue 1.
Transcribed Image Text:Suppose that A is an n x n matrix satisfying A² = In. Let P = ½-½(L, − A) - Mark only correct statements. a. The only possible eigenvalues of A are 1 and -1. b. The generalized eigenspaces of the matri A equal to the corresponding eigenspaces of A. O c. The null space of P is the eigenspace of A corresponding to the eigenvalue - 1. Od. The matrix A may not be diagonalizable. The null space of P is the eigenspace of A corresponding to the eigenvalue 1.
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