Matrix Operations

2. Examples:
   

   1. $\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}^T = \begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6\end{bmatrix}$

   2. $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}^T = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$.

   3. $\begin{bmatrix} 🔴 \\ 🟡 \\ 🟢 \end{bmatrix}^T = \begin{bmatrix} 🔴 & 🟡 & 🟢 \end{bmatrix}$.

   4. $\begin{bmatrix} a & b \\ 0 & c \end{bmatrix}^T = \begin{bmatrix} a & 0 \\ b & c \end{bmatrix}$.

   Fun Class Activity:
   1. What does example 2 tell you about the transpose of an identity matrix (or diagonal matrices)?
   2. What does example 3 tell you about the connection between row vectors and column vectors?
   3. What does example 3 tell you about the connection between upper triangular matrices and lower triangular matrices?
   4. Compute the transpose of
      $A = \begin{bmatrix} 2 & 7 & -1 & 5 \\ 3 & 4 & 8 & -3 \end{bmatrix}$
      .