Chapter 6
I understand you're looking for solutions to of I.N. Herstein's Topics in Algebra (typically covering Vector Spaces ), likely in PDF format.
Solution outline:
Suppose ( v = \sum a_i v_i = \sum b_i v_i ). Then ( \sum (a_i - b_i) v_i = 0 ). By linear independence, ( a_i - b_i = 0 ) for all ( i ), so ( a_i = b_i ). Hence unique.
Matrices
: Representation of linear transformations as matrices.
Exercises and Solutions
I.N. Herstein's Topics in Algebra
Chapter 6 of focuses on Linear Transformations . While Herstein's original text does not include a back-of-the-book answer key, various community-driven and academic solutions exist in PDF format to help students navigate its notoriously difficult problems. Key Topics in Chapter 6