Author: Prof. Dr. Fazal Rehman

Question 1: \[ \text{Evaluate } \lim_{x \to 0} \frac{\sin(x) – x}{x^3}. \] \[ \text{(a) } -\frac{1}{6}, … Very hard calculus questionsRead more

\[ \text{Question 1:} \] \[ \text{Which of the following methods is not used to solve nonlinear … MCQs – Solutions of Equations in One VariableRead more

\[ \text{Question 1: If } f(x) = e^x + \ln(x), \text{ find the second derivative } … MCQs on Mathematical Preliminaries and Error AnalysisRead more

Question # 1 (Covering: The determinant of an identity matrix is always 1.) \[ \textbf{Question: Calculate … Properties of Determinants ExerciseRead more

[latex] \[ \textbf{Q#1: Compute the Kronecker Product of the following matrices:} \] \[ A = \begin{pmatrix} … Kronecker Product ExerciseRead more

Q1: Find the Conjugate of Matrix A, where: A = [(2 + 3i, 4 – i), … Conjugate and Hermitian Matrices Exercise with solutionRead more

\[ \textbf{Exercise: Transpose of a Matrix} \] \[ \textbf{Q1: Find the Transpose of Matrix A, where:} … Transpose of a Matrix ExerciseRead more

\[ \textbf{Q1: Multiply the Scalar 3 by the Matrix A, where:} \] \[ A = \begin{pmatrix} … Scalar Multiplication of Matrices Exercise with solutionRead more

[latex] \[ \textbf{Exercise: Multiplication of Matrices} \] \[ \textbf{Q1: Multiply the Square Matrices A and B, … Multiplication of Matrices Exercise with SolutionRead more

\[ \textbf{Exercise on Division of Matrices with Step-by-Step Solutions} \] \[ \textbf{Divide the matrix } A … Division of Matrices ExerciseRead more

\[ \begin{array}{|c|c|} \hline \textbf{Matrix Subtraction Question} & \textbf{Answer} \\ \hline \text{Subtract the following Row Matrices:} \\ … Subtraction of Matrices Exercise (with Solution)Read more

  \[ \textbf{Matrix Addition Questions} \] \[ \textbf{Q1: Add the following Row Matrices:} \] \[ A … Addition of Matrices Exercise (with Solution)Read more