Questions: A=(3 -2 1 0 3 -2) calcule la traspuesta

A=(3 -2 1
0 3 -2)

calcule la traspuesta

Transcript text: $A=\left(\begin{array}{ccc}3 & -2 & 1 \\ 0 & 3 & -2\end{array}\right)$ calcule la traspuesta

Solution

To find the transpose of a matrix, we need to swap its rows with its columns. This means that the element at position (i, j) in the original matrix will be at position (j, i) in the transposed matrix.

Paso 1: Definir la matriz original \( A \)

La matriz original \( A \) es: \[ A = \begin{pmatrix} 3 & -2 & 1 \\ 0 & 3 & -2 \end{pmatrix} \]

Paso 2: Calcular la traspuesta de \( A \)

Para encontrar la traspuesta de \( A \), intercambiamos las filas por las columnas. Esto significa que el elemento en la posición \((i, j)\) en la matriz original estará en la posición \((j, i)\) en la matriz traspuesta.

La matriz traspuesta \( A^T \) es: \[ A^T = \begin{pmatrix} 3 & 0 \\ -2 & 3 \\ 1 & -2 \end{pmatrix} \]

Respuesta Final

\[ \boxed{ A^T = \begin{pmatrix} 3 & 0 \\ -2 & 3 \\ 1 & -2 \end{pmatrix} } \]

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