linear algebra Prove your answers to the following:Consider a square matrix A.a. What is the relationship among ker( A) and ker( A?)? Are they necessarily equal? Is one of them necessarilycontained in the other? More generally, what can you say about ker(A), ker( A), ker(A'), . . .?b. What can you say about im(A), im(A?), im(A'), ...?

Let A be a square matrix of order n. Then ker(A)=x∈ℝn/Ax=0 and Im(A)=Ax/x∈ℝn

Answered: Prove your answers to the following:…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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linear algebra

Prove your answers to the following:
Consider a square matrix A.
a. What is the relationship among ker( A) and ker( A?)? Are they necessarily equal? Is one of them necessarily
contained in the other? More generally, what can you say about ker(A), ker( A), ker(A'), . . .?
b. What can you say about im(A), im(A?), im(A'), ...?

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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