\[ \begin{array}{|c|c|} \hline \textbf{Matrix Equality Question} & \textbf{Equality (Yes/No)} \\ \hline A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, B = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} & ? \\ \hline C = \begin{pmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{pmatrix}, D = \begin{pmatrix} … Read more
Mention the dimension for each of the following matrix. [latex] \[ \begin{array}{|c|c|} \hline \textbf{Question} & \textbf{Dimensions: ?} \\ \hline A = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} & ? \\ \hline B = \begin{pmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \\ … Read more
Exercise [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Symmetric or Skew-Symmetric?} \\ \hline \begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 3 & 4 & 5 \\ 4 & 6 & 7 \\ 5 & 7 & … Read more
Exercise: [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Zero Matrix?} \\ \hline \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 0 & 0 \\ 0 … Read more
Exercise: [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Identity Matrix?} \\ \hline \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 0 & 0 & 0 \\ 0 … Read more
Exercise: [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Scalar Matrix?} \\ \hline \begin{pmatrix} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{pmatrix} & ? … Read more
Exercise: [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Diagonal Matrix?} \\ \hline \begin{pmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix} & ? … Read more
Exercise [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Square Matrix?} \\ \hline \begin{pmatrix} 2 & 4 & 6 \\ 1 & 3 & 5 \\ 7 & 8 & 9 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 2 & 3 \\ 4 … Read more
<h2>Exercise</h2> Suggest type of matrix for each of the followings; [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Type (Row/Column)} \\ \hline \begin{pmatrix} 2 & 4 & 6 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 \\ 3 \\ 5 \end{pmatrix} & ? \\ \hline \begin{pmatrix} -1 & 0 & 2 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 7 … Read more
\[ \textbf{Difficult MCQs on Group Theory and Applications with Answers} \] \[ \textbf{Q1: Which of the following is a group under matrix multiplication?} \] \[ \text{(A) The set of all \(2 \times 2\) invertible matrices} \] \[ \text{(B) The set of all \(2 \times 2\) matrices} \] \[ \text{(C) The set of all \(2 \times … Read more
\[ \textbf{Difficult MCQs on Mathematical Ecology with Answers} \] \[ \textbf{Q1: In the Lotka-Volterra predator-prey model, which of the following equations represents the prey population growth?} \] \[ \text{(A) } \frac{dN}{dt} = rN – \alpha NP \] \[ \text{(B) } \frac{dP}{dt} = \beta NP – \gamma P \] \[ \text{(C) } \frac{dN}{dt} = rN \] … Read more
\[ \textbf{Difficult MCQs on Python for Scientific Computing with Answers} \] \[ \textbf{Q1: Which of the following is the correct method to generate a random number between 0 and 1 using NumPy?} \] \[ \text{(A) } \text{random() } \text{from random module} \] \[ \text{(B) } \text{np.random.random()} \] \[ \text{(C) } \text{np.random.uniform(0, 1)} \] \[ \text{(D) … Read more