Answer to Question #98303 in Linear Algebra for Joshua

Question

The transpose of matrix (begin{bmatrix}1&0&-7 0&-2&3 4&5&6 end{bmatrix})
a.(begin{bmatrix}1&0&4 0&-2&5 -7&3&6 end{bmatrix})
b.(-83)
c.(-59)
d.(begin{bmatrix}-1&0&-4 0&2&-5 7&-3&-6 end{bmatrix})

Answer 1

To obtain the transposed matrix we simply reflect its elements along its main diagonal. To be more precise, the element of the $i$ -th row and $j$ -th column is replaced with the element of the $j$ -th row and $i$ -th column. Doing that we obtain:

$\begin{bmatrix}1&0&-7\\ 0&-2&3\\ 4&5&6 \end{bmatrix}^T = \begin{bmatrix} 1&0&4 \\ 0&-2&5 \\ -7&3&6\end{bmatrix}$

So the answer is a