Arulmigu Meenakshi Amman college of Engineering
Vadamavandal-604410.
Prepared by,
V.Umapathy,
Prof./Mech.
Important Questions and Answers
MA25C02- Linear Algebra
Syllabus
1. Vector Spaces: Introduction to Vector Spaces, Examples, Subspaces, Linear Combinations,
Span, Generating Sets, Linear Dependence and Independence, Basis and Dimension,
Dimension of Subspaces.
Activities: Open-Source software, exercises to test linear dependence and independence
using rank, compute span and basis of a set of vectors, determine the dimension of
subspaces, and illustrate the concept of subspace and basis in with visualization.
2. Linear Transformations and Diagonalization: Null space, Range, Dimension Theorem
(statement only), Matrix representation of a linear transformation, Eigenvalues &
Eigenvectors, Diagonalizability.
Activities: Open-Source software, exercises to compute the matrix representation of a linear
transformation, find the null space and range of a matrix, and compute eigenvalues and
eigenvectors of a matrix.
orthogonalization, Simple problems (up to 𝑹𝟑).
3. Inner Product Spaces: Inner product, Norms, Cauchy, Schwarz inequality, Gram, Schmidt
Activities: Open-Source software, exercises to compute inner products and vector norms.
4. Matrix Decomposition: Orthogonal transformation of a symmetric matrix to diagonal form
squares solutions- simple problems (up to 3×3 𝑚𝑎𝑡𝑟𝑖𝑐𝑒𝑠).
- Positive definite matrices, QR decomposition, Singular Value Decomposition (SVD), Least
Activities: Open-Source software, exercises to check if a matrix is positive definite, perform
QR decomposition and SVD using built-in functions.
S.No. Description
Unit-I
Vector Spaces
Introduction
,
,
,
Vadamavandal-604410.
Prepared by,
V.Umapathy,
Prof./Mech.
Important Questions and Answers
MA25C02- Linear Algebra
Syllabus
1. Vector Spaces: Introduction to Vector Spaces, Examples, Subspaces, Linear Combinations,
Span, Generating Sets, Linear Dependence and Independence, Basis and Dimension,
Dimension of Subspaces.
Activities: Open-Source software, exercises to test linear dependence and independence
using rank, compute span and basis of a set of vectors, determine the dimension of
subspaces, and illustrate the concept of subspace and basis in with visualization.
2. Linear Transformations and Diagonalization: Null space, Range, Dimension Theorem
(statement only), Matrix representation of a linear transformation, Eigenvalues &
Eigenvectors, Diagonalizability.
Activities: Open-Source software, exercises to compute the matrix representation of a linear
transformation, find the null space and range of a matrix, and compute eigenvalues and
eigenvectors of a matrix.
orthogonalization, Simple problems (up to 𝑹𝟑).
3. Inner Product Spaces: Inner product, Norms, Cauchy, Schwarz inequality, Gram, Schmidt
Activities: Open-Source software, exercises to compute inner products and vector norms.
4. Matrix Decomposition: Orthogonal transformation of a symmetric matrix to diagonal form
squares solutions- simple problems (up to 3×3 𝑚𝑎𝑡𝑟𝑖𝑐𝑒𝑠).
- Positive definite matrices, QR decomposition, Singular Value Decomposition (SVD), Least
Activities: Open-Source software, exercises to check if a matrix is positive definite, perform
QR decomposition and SVD using built-in functions.
S.No. Description
Unit-I
Vector Spaces
Introduction
,
,
,
