find the transpose of the matrix `A=[{:(1,3,-4),(0,2,1):}].`

Explanation

To find the transpose of the matrix \( A = \begin{pmatrix} 1 & 3 & -4 \\ 0 & 2 & 1 \end{pmatrix} \), we will follow these steps:

### Step 1: Identify the elements of the matrix
The given matrix \( A \) has two rows and three columns:
- Row 1: \( (1, 3, -4) \)
- Row 2: \( (0, 2, 1) \)

### Step 2: Understand the concept of transpose
The transpose of a matrix is obtained by swapping its rows and columns. If \( A \) is an \( m \times n \) matrix, then the transpose \( A^T \) will be an \( n \times m \) matrix.

### Step 3: Write down the transpose
To find the transpose \( A^T \):
- The first column of \( A^T \) will be the first row of \( A \): \( (1, 3, -4) \)
- The second column of \( A^T \) will be the second row of \( A \): \( (0, 2, 1) \)

Thus, we can write:
\[ A^T = \begin{pmatrix} 1 & 0 \\ 3 & 2 \\ -4 & 1 \end{pmatrix} \]

### Step 4: Final result
The transpose of the matrix \( A \) is:
\[ A^T = \begin{pmatrix} 1 & 0 \\ 3 & 2 \\ -4 & 1 \end{pmatrix} \]

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