How many of the following are true?Let I. A be a matrix of type nxn as the real variable. If c is an eigenvalue of A then det(A-c.l)# 0II. Let A be a matrix of type nxn with real variables. If A is diagonalizable, the matrix that diagonalizes A is unique.III. Each matrix is a root of its character polynomial.IV. Let T:V-> W be a linear transformation and length(V) = length (W). Then T is one-to-one if and only if T issurjective.V.T:There is a representation matrix of T, where V-> W is a linear transformation.

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How many of the following are true? Let I. A be a matrix of type nxn as the real variable. If c is an eigenvalue of A then det(A-c.I)# 0 II. Let A be a matrix of type nxn with real variables. If A is diagonalizable, the matrix that diagonalizes A is unique. II. Each matrix is a root of its character polynomial. IV. Let T:V-> W be a linear transformation and length(V) = length (W). Then T is one-to-one if and only if T is surjective. V.T:There is a representation matrix of T, where V-> W is a linear transformation.

How many of the following are true? Let I. A be a matrix of type nxn as the real variable. If c is an eigenvalue of A then det(A-c.I)# 0 II. Let A be a matrix of type nxn with real variables. If A is diagonalizable, the matrix that diagonalizes A is unique. II. Each matrix is a root of its character polynomial. IV. Let T:V-> W be a linear transformation and length(V) = length (W). Then T is one-to-one if and only if T is surjective. V.T:There is a representation matrix of T, where V-> W is a linear transformation.

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 29EQ

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