See the pic please (3) An Cnan)-matrix A over a field K that is diagonelizable over Kis also trigonalizableO True. If K is alge braically closed, then dingonaliable andover k.trigonalizable matrices are one and the same.O True. Diagonel metrices are special Kinds of twiengular ma-trices, so if A is similar to a dingonel metrix, it is inParticulur similar to a triangular matrix.© False. For example, one can check that the real [2u2) -matrxA= L% oJ has eigenyelues t1, so A is similar to Ethe dia-gonel matorx Lo ad, However, A has noazero en twies bothabove and below the main diagoual, so it is aot triganalizable.d) False This is not true in general, but it is true for exampleif k is algebraicelly cloved Cin which case every squereover k is trigonelibable).3.

Given:An nxn matrix A over a field K that is diagonalizable over K is also trigonalizable over K.To…

(3 An Inan)-matrix A over a field K that is diagonelizable over K is also trigonalizable over K. O True. If K is alge braically closed, then diegonolizakle and trigonalizable and the same. O True. Diagonel metrices are special kinds of toriengular ma- trices, so if A is similar to a dingonel metrik, ib is in Par ticular similar to a triangular matrix. O False. For example, one can check that the real 22) -matrex Matrices are one A= Lů oJ has eigeayelues Id, so A is similar to Eihe dia- gonel matrix Londo However, A has nonzero ea tries both alowe and below the main diagoad, so it is kit trigonalizable. @) False. This is not true in general, but it is true for example if k is algebraically claved Cin which caie every squlve over k is trigonelizeble). metrix

(3 An Inan)-matrix A over a field K that is diagonelizable over K is also trigonalizable over K. O True. If K is alge braically closed, then diegonolizakle and trigonalizable and the same. O True. Diagonel metrices are special kinds of toriengular ma- trices, so if A is similar to a dingonel metrik, ib is in Par ticular similar to a triangular matrix. O False. For example, one can check that the real 22) -matrex Matrices are one A= Lů oJ has eigeayelues Id, so A is similar to Eihe dia- gonel matrix Londo However, A has nonzero ea tries both alowe and below the main diagoad, so it is kit trigonalizable. @) False. This is not true in general, but it is true for example if k is algebraically claved Cin which caie every squlve over k is trigonelizeble). metrix

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 32EQ

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