Questions: After finding the transpose of matrix (A) below, locate the value of (a42^T). [ left[beginarraycccccc 13 6 2 4 7 8 11 15 3 0 9 12 endarrayright] ] (a42^T=textEx:0 0)

Solution Steps

To find the value of \( a_{42}^{T} \) in the transpose of matrix \( A \), we need to first transpose the given matrix \( A \). The transpose of a matrix is obtained by swapping its rows and columns. Once we have the transposed matrix, we can locate the value at the 4th row and 2nd column of the transposed matrix.

The given matrix \( A \) is defined as follows: \[ A = \begin{bmatrix} 13 & 6 & 2 & 4 & 7 & 8 \\ 11 & 15 & 3 & 0 & 9 & 12 \end{bmatrix} \]

The transpose of matrix \( A \), denoted as \( A^T \), is obtained by swapping the rows and columns: \[ A^T = \begin{bmatrix} 13 & 11 \\ 6 & 15 \\ 2 & 3 \\ 4 & 0 \\ 7 & 9 \\ 8 & 12 \end{bmatrix} \]

To find the value of \( a_{42}^{T} \), we look for the element in the 4th row and 2nd column of the transposed matrix \( A^T \): \[ a_{42}^{T} = A^T[3, 1] = 0 \]

Final Answer