**Introduction to Linear Algebra: Gilbert Strang** | **Problem Set 1.2 Solutions**

Introduction to linear algebra

Gilbert Strang

fifth edition

Massachusetts Institute of Technology

Linear Algebra is a wing of mathematics dealing with vectors, matrices, determinants, equations, n-Dimensional vectors. Linear algebra has a wide application in the fields of science, engineering, computer science. Gilbert Strang an American mathematician who has made many contributions to mathematics education is well known for his Book ” Introduction to Linear Algebra”.

Introduction to linear Algebra Contains a collection of good problems. Helpful for a better understanding of the topics. Here are well explained solution to all the Problem Sets of Introduction to Linear Algebra.

Chapter 1Introduction to Vectors

1.2 Lengths and Dot Products

REVIEW OF THE KEY IDEAS1. The dot productmultiplies each componentv•wbyv_{i}and adds allw_{i}. 2. The length ||v_{i}w_{i}|| is the square root ofv. Thenv·v=u/||v||vis a: length 1. 3. The dot product isunit vector= 0 when vectorsv·wandvare perpendicular. 4. The cosine of \theta (the angle between any nonzerowandv) never exceeds I:wCosinecos\theta = \frac{v.w}{||v|| ||w||}|v.w| \le ||v|| ||w||Schwarz inequality

**Problem Set 1.2** *page-no 18*

Problem Set 1.2 explained solutions of Introduction to linear algebra, author Gilbert Strang. All solved questions of the fifth edition.