\[ \textbf{Exercise: Transpose of a Matrix} \] \[ \textbf{Q1: Find the Transpose of Matrix A, where:} \] \[ A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix} \] \[ \textbf{Solution:} \] \[ A^T = \text{Transpose of } A = \begin{pmatrix} 1 & 4 \\ 2 & 5 \\ 3 … Read more

\[ \textbf{Q1: Multiply the Scalar 3 by the Matrix A, where:} \] \[ A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \] \[ \textbf{Solution:} \] \[ 3 \cdot A = 3 \cdot \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \] \[ = \begin{pmatrix} 3 \cdot 1 & 3 \cdot 2 … Read more

[latex] \[ \textbf{Exercise: Multiplication of Matrices} \] \[ \textbf{Q1: Multiply the Square Matrices A and B, where:} \] \[ A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix} \] Solution \[ \textbf{Q2: Multiply the Diagonal Matrices A and B, where:} \] … Read more

\[ \textbf{Exercise on Division of Matrices with Step-by-Step Solutions} \] \[ \textbf{Divide the matrix } A = \begin{pmatrix} 6 & 3 \\ 9 & 12 \end{pmatrix} \textbf{ by the matrix } B = \begin{pmatrix} 3 & 1 \\ 3 & 4 \end{pmatrix}. \] Solution \[ \textbf{ Divide the Square Matrix A by the Square Matrix … Read more

\[ \begin{array}{|c|c|} \hline \textbf{Matrix Subtraction Question} & \textbf{Answer} \\ \hline \text{Subtract the following Row Matrices:} \\ A = \begin{pmatrix} 5 & 7 \end{pmatrix}, B = \begin{pmatrix} 3 & 4 \end{pmatrix} & ? \\ \hline \text{Subtract the following Column Matrices:} \\ A = \begin{pmatrix} 9 \\ 10 \end{pmatrix}, B = \begin{pmatrix} 4 \\ 5 \end{pmatrix} & … Read more

  \[ \textbf{Matrix Addition Questions} \] \[ \textbf{Q1: Add the following Row Matrices:} \] \[ A = \begin{pmatrix} 1 & 2 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 4 \end{pmatrix} \] \[ \textbf{Q2: Add the following Column Matrices:} \] \[ A = \begin{pmatrix} 5 \\ 6 \end{pmatrix}, \quad B = \begin{pmatrix} 7 \\ 8 \end{pmatrix} … Read more

\[ \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