\[ \newcommand{\parallelsym}{\mathbin{\!/\mkern-5mu/\!}} \newcommand{\tr}{\operatorname{tr}} \] This is a set of problems with which you can take exercise on linear algebra. Day 1. The problems for the first day are related to: Representation of Linear Transformations. Explain why every linear transformation between finite dimensional vector spaces can be regarded as a matrix. (Hint: Consider bases for domain and codomain of the transformation.) Use matrix multiplication to …
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Inner Product
This set of exercises is retrieved from the seventh chapter of Linear Algebra by Robert J. Valenza. Note that these solutions are not fully elaborated; You have to fill the descriptions by yourself. Problem 7.1 In \(\mathbb{R}^3,\) compute the inner product of \((1,\,2,\,-1)\) and \((2,\,1,\,4).\) What is the length of each vector? What is the angle between these vectors? Solution. The lengths of given …