Problems, Theory and Solutions in Linear Algebra Part 1 Euclidean Space
Publisher: Bookboon
Published: 2015
ISBN-13: 9788740311341
Table of contents: title: Content; title: 1. Vectors, lines and planes in R^3; title: 1.1. Vector operations and the dot product; title: 1.2. The cross product; title: 1.3. Planes and their equations; title: 1.4. Lines and their parametrizations; title: 1.5. More on planes and lines; title: 1.6. Exercises; title: 2. Matrix algebra and Gauss elimination; title: 2.1. Matrix operations of addition and multiplications; title: 2.2. The determinant of square matrices; title: 2.3. The inverse of square matrices; title: 2.4. Gauss elimination for systems of linear equations; title: 2.5. Square systems of linear equations; title: 2.6. Systems of linear equations in R^3; title: 2.7. Intersection of lines in R^3; title: 2.8. Exercises; title: 3. Spanning sets and linearly independent sets; title: 3.1. Linear combinations of vectors; title: 3.2. Spanning sets of vectors; title: 3.3. Linearly dependent and independent sets of vectors; title: 3.4. Exercises; title: 4. Linear transformations in Euclidean spaces; title: 4.1. Linear transformations: domain and range; title: 4.2. Standard matrices and composite transformations; title: 4.3. Invertible linear transformations; title: 4.4. Exercises