I need help on my linear algebra 17. For A =show that the mapping ada : M2 (R) → M2 (R) defined by ad4 (B)AB – BĀ is a linear transformation. Find bases for the kernel and the range of ad4.

First we will find the value of AB-BA

Answered: 7. For A = show that the mapping ada :…

7. For A = show that the mapping ada : M2 (R) → M2 (R) defined by ad A (B) AB – BÃ is a linear transformation. Find bases for the kernel and the range of ad4. -

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 5EQ: In Exercises 1-12, determine whether T is a linear transformation. 5. T:Mnn→ ℝ defined by...

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Question

I need help on my linear algebra

1
7. For A =
show that the mapping ada : M2 (R) → M2 (R) defined by ad4 (B)
AB – BĀ is a linear transformation. Find bases for the kernel and the range of ad4.

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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