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A- [*] -2 -20 (a) Compute det(A). (b) Compute rank(A) and nullity(A). (c) Are the columns of A linearly independent? (d) Compute A-!. (e) Find the eigenvalues of A. (f) For each eigenvalue of A, find a corresponding eigenvector. (g) Find an invertible matrix P and a diagonal matrix D such that A = PDP-1. (h) Find all solutions to the equation 3 A

A- [*] -2 -20 (a) Compute det(A). (b) Compute rank(A) and nullity(A). (c) Are the columns of A linearly independent? (d) Compute A-!. (e) Find the eigenvalues of A. (f) For each eigenvalue of A, find a corresponding eigenvector. (g) Find an invertible matrix P and a diagonal matrix D such that A = PDP-1. (h) Find all solutions to the equation 3 A

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 38EQ
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[ -2 -20 A = 7 (a) Compute det(A). (b) Compute rank(A) and nullity(A). (c) Are the columns of A linearly independent? (d) Compute A-!. (e) Find the eigenvalues of A. (f) For each eigenvalue of A, find a corresponding eigenvector. (g) Find an invertible matrix P and a diagonal matrix D such that A = PDP-1. (h) Find all solutions to the equation 3 A = 2
Transcribed Image Text:[ -2 -20 A = 7 (a) Compute det(A). (b) Compute rank(A) and nullity(A). (c) Are the columns of A linearly independent? (d) Compute A-!. (e) Find the eigenvalues of A. (f) For each eigenvalue of A, find a corresponding eigenvector. (g) Find an invertible matrix P and a diagonal matrix D such that A = PDP-1. (h) Find all solutions to the equation 3 A = 2
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