# Linear Algebra Study Materials 2021 – Download B.Sc Mathematics Study Notes PDF

Download **Linear Algebra** **Study Materials 2021**. In this article, we are going to provide Study Notes for the School of Sciences. This subject will come mostly for * B.Sc (Mathematics). *You can download these books from our

**Exams Time**website that is free of cost. We have provided the materials for the important aspects of Vector Spaces,

**Linear Transformations and Matrices**, Eigen Values and Eigen Vectors, etc.

__Mathematics__

*students*can download these Study Materials which will be useful for their Exam Preparation.

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Table of Contents

## Linear Algebra Study Materials

Name of the Subject | Linear Algebra |

Category | School of Sciences |

Useful for | Bachelor of Science |

Course Type | Under Graduation Courses |

Article on | Linear Algebra Study Materials 2021 |

Study Material Format | |

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## Fundamentals of Linear Algebra Study Books

Here is the list of topics in Linear Algebra Study Materials :

Here are the books related to Linear Algebra Study Materials :

Subject | Download Links |

Linear Algebra | Download |

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## Linear Algebra Study Notes

Subject | Download Links |

Linear Algebra | Download |

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### Chapters & Topics

Here is the list of topics in Linear Algebra Study Materials :

**Vector Spaces**

- Basis and Dimension
- Vector Spaces
- Two – and Three – Dimensional Spaces
- Sets, Functions, and Fields

**Linear Transformations and Matrices**

- Matrices – II
- Matrices – I
- Linear Transformations – II
- Linear Transformations – I

**Eigenvalues and Eigenvectors**

- Characteristic and Minimal Polynomial
- Eigenvalue and Eigenvectors
- Determinants

**Inner Products and Quadratic Forms**

- Conics
- Real Quadratic Forms
- Hermitian and Unitary Operators
- Inner Product Spaces

## Subject in the Universities

This subject will be useful to the students who are pursuing a Bachelor of Science. The following university students can also download **Linear Algebra **study materials :

- IGNOU
- Uttarakhand Open University
- University of Calicut
- Pondicherry University

### Subject in the Semesters

**Linear Algebra **subject will be studied by the students in the following semesters of their respective courses :

- B.Sc Mathematics III Semester

## Unit wise PDFs – Linear Algebra Study Materials

Download Unit wise PDFs of** Linear Algebra **subject :

Units | Download Links |

Vector Spaces | Download |

Linear Transformations and Matrices | Download |

Eigenvalues and Eigenvectors | Download |

Inner Products and Quadratic Forms | Download |

### Important Questions

We have mentioned some of the important questions of **Linear Algebra **subject :

- Express the line ax + by = c in R² in parametric form.
- Express the line with vector form (x, y)T = (1, −1)T + t(2, 3)T in the form ax + by = c.
- Find the line through points a and b in the following cases:
- a = (1, 1, −3)T and b = (6, 0, 2)T and
- a = (1, 1, −3, 4)T and b = (6, 0, 2, −3)T

- Find the line of intersection of the planes 3x − y + z = 0 and x − y − z = 1 in parametric form.
- Find the equation in vector form of the line through (1, −2, 0)T parallel to (3, 1, 9)Τ.
- Determine whether or not the lines (x, y, z)T = (1, 2, 1)T + t(1, 0, 2)T and (x, y, z) T = (2, 2, −1)T + t(1, 1, 0)T

intersect. - Find an equation for the plane in R³ through the points (6, 1, 0)T, (1, 0, 1)T and (3, 1, 1)T.
- Compute the intersection of the line through (3, −1, 1)T and (1, 0, 2)T with the plane ax + by + cz = d when
- a = b = c = 1, d = 2,
- a = b = c = 1 and d = 3.

- Verify the four properties of the dot product on R³.
- Show that for any a and b in R³ |a + b|² − |a − b|² = 4a · b.
- Prove the vector version of Pythagoras’s Theorem. If c = a + b and a · b = 0, then |c|² = |a|² + |b|².
- Find the orthogonal decomposition (1, 1, 1)T = a + b, where a lies on the plane P with equation 2x + y + 2z = 0 and a · b = 0. What is the orthogonal projection of (1, 1, 1)T on P?
- Consider any two lines in R³. Suppose I offer to bet you they don’t intersect. Do you take the bet or refuse it? What would you do if you knew the lines were in a plane?
- Find the distance from the point (1, 1, 1)T to
- the plane x + y + z = 1, and
- the plane x − 2y + z = 0.

- Verify the Parallelogram Law (in R³) by computing where the line through a parallel to b meets the line through
**b**parallel to**a**

## Recommended Books for Linear Algebra

The books that are referred to and recommended by toppers are given below. For more information refer to other authors’ books also.

- Theory and Problems of Linear Algebra by Ritu Jain R.D. Sharma
- Schaum’s Outline Of Beginning Linear Algebra by Seymour Lipschutz
- Linear Algebra and Its Applications by Gilbert Strang
- Linear Algebra | Second Edition | By Pearson by Kenneth M Hoffman

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