16) This is linear algebra ! write neatly, answer only. Show your work! (a) Find the algebraic multiplicity ofnumerical value only.)=-8 as an eigenvalue of A. (Enter the(b) Find the dimension of the eigenspace corresponding to λ = -8. (Enter thenumerical value only.)(c) Is A diagonalizable? (Enter "yes" or "no" only.) For the matrix A=T-80 0 0000-810001600 0 0 179one of its eigenvalues isλ = -8.(a) Find the algebraic multiplicity of A = -8 as an eigenvalue of A. (Enter the=numerical value only.)

Answered: Image /qna-images/answer/fc2b4d0b-0599-4242-b46a-1d9befcc42bf.jpg

(a) Find the algebraic multiplicity of λ = -8 as an eigenvalue of A. (Enter the numerical value only.) (b) Find the dimension of the eigenspace corresponding to A = -8. (Enter the numerical value only.) A/ (c) Is A diagonalizable? (Enter "yes" or "no" only.) A

(a) Find the algebraic multiplicity of λ = -8 as an eigenvalue of A. (Enter the numerical value only.) (b) Find the dimension of the eigenspace corresponding to A = -8. (Enter the numerical value only.) A/ (c) Is A diagonalizable? (Enter "yes" or "no" only.) A

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 31EQ

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Question

16) This is linear algebra ! write neatly, answer only. Show your work!

(a) Find the algebraic multiplicity of
numerical value only.)
=
-8 as an eigenvalue of A. (Enter the
(b) Find the dimension of the eigenspace corresponding to λ = -8. (Enter the
numerical value only.)
(c) Is A diagonalizable? (Enter "yes" or "no" only.)

For the matrix A
=
T-8
0 0 0
00
0
-8
1
0
0
0
16
0
0 0 0 17
9
one of its eigenvalues is
λ = -8.
(a) Find the algebraic multiplicity of A = -8 as an eigenvalue of A. (Enter the
=
numerical value only.)

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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