Linear Algebra and Complex variable

Daffodil International University Department of Electrical and Electronic Engineering Faculty of Engineering Mid-Term Examination, Fall - 2026 Course Code: 0541-113 Course Title: Linear Algebra and Complex Variable Section: A, B, C, D, R Level-Term: L1-T1 Teacher's Initial: HRP Full Marks: 25 Date: November 02, 2026 Time: 1.5 Hours [Answer all the following questions] [The second right-most column indicates the COs with the respective Bloom's level] [The right-most column indicates the assigned marks] Q1. a) Explain the following with example CO-1 (C2) [2] i) Augmented Matrix ii) Hermitian Matrix b) Identify whether the following system of linear equations is consistent or inconsistent. CO-1 (C2) [3] x + y + z = -3 3x + y - 2z = -2 2x + 4y + 7z = 7 Q2. a) Categorize the values of 'λ' for which the following system of linear equations has CO-1 (C2) [5] i) No solution ii) Infinitely many solutions iii) Unique solution u + 2v - w = 3 3u - v + 2w = 3 4u + v + (λ^2 - 8)w = λ + 3 b) Identify the echelon form, row reduced echelon form and normal form of the following matrix CO-1 (C2) [5] M = [ 1 2 -1 3 ] [ 2 4 1 7 ] [-1 -2 2 -1 ] [ 3 6 0 8 ] Q3. a) Express P as the sum of symmetric matrix and skew-symmetric matrix, where CO-1 (C2) [5] P = [ cos 0° | (d^2/dt^2 (t^3 + 2t^2))|_{t=1} - 16 | e^0 - 1 ] [ log_10 100^-2 | |( 1 2 )|^T | lim_{t->2} (t + 2) ] [ | |( 3 2 )| | ] [ √4 - 2 | 3! / 2! - 3 | 1 - 2 | -2^-1 | ] b) Using only elementary row transformations to reduce W to I, identify the inverse of W, where CO-1 (C2) [5] W = [ 1 -2 3 ] [ 2 3 -1 ] [ -3 1 2 ]