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 1
Introduction to Vectors
1.2 Lengths and Dot Products

 REVIEW OF THE KEY IDEAS
1. The dot product v•w multiplies each component vi by wi and adds all viwi.
2. The length ||v|| is the square root of v·v. Then u = v/||v|| is a unit vector: length 1.
3. The dot product is v·w= 0 when vectors v and w are perpendicular.
4. The cosine of  \theta  (the angle between any nonzero v and w) never exceeds I:
      Cosine   cos\theta  =  \frac{v.w}{||v|| ||w||}   Schwarz inequality   |v.w|  \le  ||v|| ||w|| 

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.