# 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.

## 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 PDF Download Other Study Materials Click Here

## 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 :

## Linear Algebra Study Notes

### 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

Related Posts
• Matrices – II
• Matrices – I
• Linear Transformations – II
• Linear Transformations – I

Eigenvalues and Eigenvectors

• Characteristic and Minimal Polynomial
• Eigenvalue and Eigenvectors
• Determinants

• Conics
• 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

### 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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