QuestionQuestion Computer $A^{T}$ for the matrix below. $A=\left[\begin{array}{lll} 1 & 4 & 2 \\ 3 & 5 & 0 \\ 1 & 2 & 3 \end{array}\right]$
Provide your answer below:

Studdy Solution

STEP 1

1. The matrix $A$ is a 3x3 matrix.
2. We need to find the transpose of matrix $A$ , denoted as $A^T$ .
3. The transpose of a matrix is obtained by swapping its rows and columns.

STEP 2

1. Identify the elements of matrix $A$ .
2. Swap the rows and columns to form $A^T$ .
3. Write the resulting transposed matrix.

STEP 3

Identify the elements of matrix $A$ :
$A = \begin{bmatrix} 1 & 4 & 2 \\ 3 & 5 & 0 \\ 1 & 2 & 3 \end{bmatrix}$

STEP 4

Swap the rows and columns to form the transpose $A^T$ . This means:
- The first row of $A$ becomes the first column of $A^T$ . - The second row of $A$ becomes the second column of $A^T$ . - The third row of $A$ becomes the third column of $A^T$ .
$A^T = \begin{bmatrix} 1 & 3 & 1 \\ 4 & 5 & 2 \\ 2 & 0 & 3 \end{bmatrix}$

STEP 5

Write the resulting transposed matrix $A^T$ :
$A^T = \begin{bmatrix} 1 & 3 & 1 \\ 4 & 5 & 2 \\ 2 & 0 & 3 \end{bmatrix}$
The transposed matrix $A^T$ is:
$\boxed{\begin{bmatrix} 1 & 3 & 1 \\ 4 & 5 & 2 \\ 2 & 0 & 3 \end{bmatrix}}$

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