Mathematics 2

Daffodil International University Faculty of Science & Information Technology Department of Multimedia and Creative Technology (MCT) Mid Term Examination, Fall - 2026 Course Code: 0541-121 Course Title: Mathematics-2 Course Teacher's Initial: AG Time: 1:30 Hrs Marks: 25 Answer ALL Questions 1. a) Construct an augmented matrix based on the system of linear equations stated in question number 4. [1+1+(1+1)=4] [CLO 1, C1] b) In a hypothetical scenario you are provided with two matrices. The first matrix has a dimension of 3 by 10 and the second matrix has a dimension of 10 by 33. Can these two matrices be multiplied following the matrix multiplication process? Start writing your answer with a "Yes" or "No". Later justify your answer briefly. c) Exemplify the following types of matrices without any definition or explanation. i. Identity Matrix ii. Upper Triangular Matrix 2. By applying the calculation process of Digital Differential Analyzer, calculate and draw lines for the following cases- [7] [CLO 2, C3] Case 1: (5, 4) to (11, 4) Case 2: (5, 4) to (5, 12) Case 3: (5, 3) to (10, 6) Case 4: (5, 5) to (10, 10) Case 5: (11, 8) to (16, 13) Note that all lines must be drawn in a single graph paper and proper labeling is critically important. 3. Calculate the determinant, cofactors, ad-joint and inverse matrix for the given system of linear equations and figure out the value of x, y & z. [7] [CLO 1, C3] 10x + 2y + 3z = 51 6x + 3y + 2z = 41 8x + y + 4z = 49 4. Apply Cramer's rule in the following system of linear equations and figure out the value of x, y & z. [7] [CLO 1, C3] 8x + 2y + 3z = 68 5x + 3y + 2z = 54 7x + y + 4z = 66