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
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.

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