BSc CSIT (TU) Science Mathematics II (BSc CSIT, MTH163) Question Paper 2080
This is the official BSc CSIT (TU) (Science stream) Mathematics II (BSc CSIT, MTH163) question paper for 2080, 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 2080 paper is a great way to practise under real exam conditions.
Section A: Long Answer Questions
Attempt any TWO questions.
Define basis and dimension of a vector space. Prove that any two bases of a finite-dimensional vector space have the same number of elements.
Find the matrix of the linear transformation (T: R^3 \rightarrow R^2) defined by (T(x,y,z) = (x+y, y-z)) with respect to the standard bases, and find its kernel and range.
Apply the Gram-Schmidt process to obtain an orthonormal basis from a given basis of (R^3) with the standard inner product.
Section B: Short Answer Questions
Attempt any EIGHT questions.
Define a basis and dimension with examples.
Find the rank of a 3x3 identity matrix.
Define a linear operator.
State the spectral theorem for symmetric matrices.
What is an orthogonal projection?
Find the eigenvectors of [[3,0],[0,3]].
Define a coordinate vector relative to a basis.
What is a diagonalizable matrix?
State two properties of eigenvalues.