Homework Help is Here – Start Your Trial Now!
Math
Algebra
4. Let L: R3 → R* be a linear transformation, if L is one-to-one, then it is onto. 5. Let L:V → W, if L(0,) = 0w then L is a linear transformation. 6. If L:V → W is a linear transformation, then for any vector w in W there is a vector v in V such that L(v) = w. 7. If P is nonsingular and D is diagonal, then the eigenvalues of A = P~'DP are the diagonal entries of D. 8. If A is an eigenvalue of A of algebraic multiplicity k, then the dimension of the eigenspace associated with a is k. 9. A matrix A is diagonalizable if all the roots of its characteristic polynomial are real. 10. Let S = {t? + 1, t – 1, t} be a basis for P2, then [t2 – t + 3]s %3D

4. Let L: R3 → R* be a linear transformation, if L is one-to-one, then it is onto. 5. Let L:V → W, if L(0,) = 0w then L is a linear transformation. 6. If L:V → W is a linear transformation, then for any vector w in W there is a vector v in V such that L(v) = w. 7. If P is nonsingular and D is diagonal, then the eigenvalues of A = P~'DP are the diagonal entries of D. 8. If A is an eigenvalue of A of algebraic multiplicity k, then the dimension of the eigenspace associated with a is k. 9. A matrix A is diagonalizable if all the roots of its characteristic polynomial are real. 10. Let S = {t? + 1, t – 1, t} be a basis for P2, then [t2 – t + 3]s %3D

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

true or false only 

answer only 4, 5, 6 , 7, 8, 9, 10

I. Answer each of the following as TRUE or FALSE. 1. There are linear transformations L:R³ → R5 that are onto. 2. If a 3 x 3 matrix A has eigenvalues a = 1, –1,3, then A is diagonalizable. 3. Let L: V → W be a linear transformation, the ker L is the set of elements in V which map into 0 e W. 4. Let L: R3 → R* be a linear transformation, if L is one-to-one, then it is onto. 5. Let L:V → W, if L(0,) = 0w then L is a linear transformation. 6. If L:V → W is a linear transformation, then for any vector w in W there is a vector v in V such that L(v) = w. 7. If P is nonsingular and D is diagonal, then the eigenvalues of A = P-1DP are the diagonal entries of D. 8. If 2 is an eigenvalue of A of algebraic multiplicity k, then the dimension of the eigenspace associated with 2 is k. 9. A matrix A is diagonalizable if all the roots of its characteristic polynomial are real. 10. Let S = {t? + 1, t – 1, t} be a basis for P2, then [t² – t + 3]s =
Transcribed Image Text:I. Answer each of the following as TRUE or FALSE. 1. There are linear transformations L:R³ → R5 that are onto. 2. If a 3 x 3 matrix A has eigenvalues a = 1, –1,3, then A is diagonalizable. 3. Let L: V → W be a linear transformation, the ker L is the set of elements in V which map into 0 e W. 4. Let L: R3 → R* be a linear transformation, if L is one-to-one, then it is onto. 5. Let L:V → W, if L(0,) = 0w then L is a linear transformation. 6. If L:V → W is a linear transformation, then for any vector w in W there is a vector v in V such that L(v) = w. 7. If P is nonsingular and D is diagonal, then the eigenvalues of A = P-1DP are the diagonal entries of D. 8. If 2 is an eigenvalue of A of algebraic multiplicity k, then the dimension of the eigenspace associated with 2 is k. 9. A matrix A is diagonalizable if all the roots of its characteristic polynomial are real. 10. Let S = {t? + 1, t – 1, t} be a basis for P2, then [t² – t + 3]s =
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer