Matrix Dimensions Exercise (with Solution)

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

Row and Column Matrices Exercise (with Solution)

<h2>Exercise</h2> Suggest type of matrix for each of the followings; [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} &amp; \textbf{Type (Row/Column)} \\ \hline \begin{pmatrix} 2 &amp; 4 &amp; 6 \end{pmatrix} &amp; ? \\ \hline \begin{pmatrix} 1 \\ 3 \\ 5 \end{pmatrix} &amp; ? \\ \hline \begin{pmatrix} -1 &amp; 0 &amp; 2 \end{pmatrix} &amp; ? \\ \hline \begin{pmatrix} 7 … Read more

Group Theory and Applications MCQs

\[ \textbf{Difficult MCQs on Group Theory and Applications with Answers} \] \[ \textbf{Q1: Which of the following is a group under matrix multiplication?} \] \[ \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

Mathematical Ecology MCQs

\[ \textbf{Difficult MCQs on Mathematical Ecology with Answers} \] \[ \textbf{Q1: In the Lotka-Volterra predator-prey model, which of the following equations represents the prey population growth?} \] \[ \text{(A) } \frac{dN}{dt} = rN – \alpha NP \] \[ \text{(B) } \frac{dP}{dt} = \beta NP – \gamma P \] \[ \text{(C) } \frac{dN}{dt} = rN \] … Read more

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