Exercise · ZW-TRANSPOSE-MATRIX-001 · ★☆☆ Basic
Compute the transpose of \(\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6\end{pmatrix}\).
Choose one option.
Show answer
- A. \(\begin{pmatrix}1 & 4 \\ 2 & 5 \\ 3 & 6\end{pmatrix}\)
Explanation
The rows of \(A\) become the columns of \(A^T\): the row \((1,2,3)\) becomes the first column and \((4,5,6)\) the second. The result is \(3\times2\).
Review the concept: Transpose matrix
The transpose \(A^T\) of a matrix \(A\) is the one obtained by exchanging its rows and columns.
\[(A^T)_{ij}=a_{ji}\]
More practice problems: transpose matrix
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- ZW-TRANSPOSE-MATRIX-005 If A and B have the same size, what is (A+B)^T equal to?
- ZW-TRANSPOSE-MATRIX-006 With A=[1 2; 0 1] and B=[3 0; 1 2], compute (AB)^T.
- ZW-TRANSPOSE-MATRIX-007 Compute A+A^T for A=[1 2; 3 4].
- ZW-TRANSPOSE-MATRIX-008 Let x=(1,-2,3)^T be a column vector. What is x^Tx?
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