Linear Algebra Past Paper 2024 | BS 4th Term UOS (MATH-202)
University: University of Sargodha (UOS)
Program: BS 4th Term
Subject: Linear Algebra (MATH-202 / MATH-3215)
Year: 2024
Time Allowed: 2 Hours 30 Minutes
Maximum Marks: 60
Why Use This Linear Algebra Past Paper?
This paper helps students understand exam style, frequently asked questions, and important Linear Algebra concepts. It includes both objective and subjective questions used in final examinations.
- Practice university-level Linear Algebra questions
- Revise matrices, vector spaces, eigenvalues, and transformations
- Improve speed and accuracy
- Understand expected answer formatting
Linear Algebra Past Paper 2024 (Complete Text)
University of Sargodha
BS 4th Term Examination 2024Subject: Computer Science
Paper: Linear Algebra (MATH-202/MATH-3215)Note: Objective part is compulsory. Attempt any three questions from subjective part.
Objective Part (Compulsory)
Q.1 Write short answers (2–3 lines each):
- Define trace of a matrix.
- Check if vectors u₁ = (1,2,−3) and u₂ = (1,−4,3) are orthogonal.
- Write bases for vector space M₂×₂.
- Show that (−1)u = −u for u ∈ V.
- If A is invertible, show Aᵀ is also invertible.
- Define Markov matrix.
- Find inverse of A = [5 3; 4 2].
- Show k0 = 0 for any scalar k.
- Show matrices with trace zero form a subspace.
- If A = [i 0; 1 −i], show A⁴ = I₂.
- Write basis of Pₙ(x).
- Define similar matrices.
Subjective Part (Attempt any Three)
Q.2 Determine basis and dimension of subspace (given vectors). Prove A satisfies its characteristic equation.
Q.3 Find basis & dimension of W. Find eigenvalues and eigenvectors of given matrix.
Q.4 Span questions, and solve system of linear equations.
Q.5 Find A⁻¹, apply Gram-Schmidt to obtain orthonormal basis.
Q.6 Diagonalize matrix and prove given set is a basis of R³.
Solved Short Questions (Toggle to View)
1. What is the trace of a matrix?
The trace of a square matrix is the sum of the elements on its main diagonal.
Reference: Wolfram MathWorld – Trace
2. Are u₁ = (1,2,−3) and u₂ = (1,−4,3) orthogonal?
Compute dot product: 1(1) + 2(−4) + (−3)(3) = 1 − 8 − 9 = −16. Since result ≠ 0, the vectors are not orthogonal.
Reference: Khan Academy – Linear Algebra
3. What is a Markov matrix?
A Markov matrix is a square matrix whose columns sum to one and all entries are non-negative.
Reference: Wikipedia – Markov Chains
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Exam Tips
- Practice solving matrix problems step-by-step
- Memorize common vector space properties
- Understand Gram-Schmidt procedure conceptually
- Review previous papers before exams
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