BSc CSIT (TU) Science Mathematics II (BSc CSIT, MTH163) Question Paper 2081
This is the official BSc CSIT (TU) (Science stream) Mathematics II (BSc CSIT, MTH163) question paper for 2081, as set in the regular annual examination. It carries 60 full marks and a time allowance of 180 minutes, across 12 questions. On Kekkei you can attempt this Mathematics II (BSc CSIT, MTH163) past paper online with a timer, get instant AI feedback and step-by-step solutions, and track the topics where you lose marks — completely free. Whether you are revising for your BSc CSIT (TU) Mathematics II (BSc CSIT, MTH163) exam or solving previous years' question papers, this 2081 paper is a great way to practise under real exam conditions.
Section A: Long Answer Questions
Attempt any TWO questions.
State the conditions for a system of linear equations to have (i) a unique solution (ii) infinitely many solutions (iii) no solution. Illustrate each with an example using the rank method.
Define a symmetric and a skew-symmetric matrix. Show that every square matrix can be expressed uniquely as the sum of a symmetric and a skew-symmetric matrix.
Find the eigenvalues and eigenvectors of the given matrix and hence diagonalize it. Use the diagonal form to compute (A^4).
Section B: Short Answer Questions
Attempt any EIGHT questions.
Define a skew-symmetric matrix with an example.
Find the determinant of [[2,1,0],[1,3,1],[0,1,2]].
Define the image and kernel of a linear map.
What is the algebraic multiplicity of an eigenvalue?
Define an inner product on (R^n).
State whether the vectors (1,2), (2,4) are linearly independent.
Define a finite-dimensional vector space.
What is the canonical form of a quadratic form?
Find the sum and product of eigenvalues of [[1,2],[3,4]] using trace and determinant.