Linear Algebra Study Materials 2020 – Download B.Sc Mathematics Study Notes PDF

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Download Linear Algebra Study Materials 2020. 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 are 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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Linear Algebra Study Materials - Download Unit wise PDFs & Imp Questions

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 Study Materials 2020
Study Material Format PDF
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Fundamentals of Linear Algebra Study Books

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 are 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 the 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

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