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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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||Study Materials 2020|
|Study Material Format|
|Download Other Study Materials||Click Here|
Fundamentals of Linear Algebra Study Books
Linear Algebra Study Notes
Chapters & Topics
Here are the list of topics in Linear Algebra Study Materials :
- 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
Inner Products and Quadratic Forms
- 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 :
- 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 :
|Linear Transformations and Matrices||Download|
|Eigenvalues and Eigenvectors||Download|
|Inner Products and Quadratic Forms||Download|
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
- 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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