Exam Details
First Quiz
The first quiz will be held on January 20 (Saturday) between 2 pm - 6 pm. The quiz will be conducted online via Mookit (https://hello.iitk.ac.in/user/login) in the diamond jubilee building and at the new core labs. The quiz will be conducted in three slots.
Slot 1 : 2:30 - 3:00 pm. Slot 2 : 3:30 - 4:00 pm Slot 3 : 4:30 - 5:00 pm
Seating arrangements and guidelines will be communicated by email.
Syllabus for Quiz 1 : Solving a system of linear equations using row reductions, Gauss-Elimination Method, Reduced Row Echelon Form, Elementary Matrices, Effect of multiplication by elementary matrices, Invertible matrices and its connection with elementary matrices, Permutation, Determinant of a matrix, Properties of determinants.
Second Quiz is scheduled on 5th February (Monday) 7 pm -7:40 pm.
Syllabus for Quiz 2:
Solution of a system of linear equations using rank (Under class notes, contents of Lecture 7 done in L18 on 19th Jan 2024, Lecture 5 done in L19 on 15th Jan 2024 and Pg. 49-51 of https://home.iitk.ac.in/~arlal/MTH102/la.pdf )
Permutation, Cycles
Vector Space, Subspace, Linearly dependent & Linearly independent vectors
Dimension of Subspaces
Intersection, Sum of subspaces and its dimension (contents of Lecture Note 9 except quotient space )
Seating Arrangement : Link
End Semester Exam is scheduled on 19th February (Monday) 6 pm - 8 pm
Syllabus for End-Sem :
Vector Space, Subspace, Linearly dependent & Linearly independent vectors, Dimension of Subspaces, Intersection, Sum of subspaces and its dimension
Quotient Space
Linear Maps between vector spaces, Rank-Nullity Theorem
Row Space, Column Space, Null Space, Rank of a Matrix
Inner Product, Cauchy-Schwartz Inequlaity, Orthogonal Vectors, Orthogonal Projection, Least square solution
Gram Schmidt orthogonalization process
Orthogonal matrices
Eigen values and eigen vectors of a matrix, Characteristic polynomial, diagonalization
Eigen values and diagonalization of a real symmetric matrix