Exercise · ZW-TRANSPOSE-MATRIX-004 · ★☆☆ Basic
If \(A^T=\begin{pmatrix}1 & 3 \\ 2 & 4\end{pmatrix}\), what is \(A\)?
Choose one option.
Show answer
- D. \(\begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}\)
Explanation
Since \((A^T)^T=A\), just transpose again: the rows of \(A^T\) are the columns of \(A\), so \(A=\begin{pmatrix}1 & 2\\ 3 & 4\end{pmatrix}\).
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
- ZW-TRANSPOSE-MATRIX-001 Compute the transpose of [1 2 3; 4 5 6].
- ZW-TRANSPOSE-MATRIX-002 If A is a 2×4 matrix, what size is A^T?
- ZW-TRANSPOSE-MATRIX-003 Which of these matrices is symmetric (satisfies A=A^T)?
- 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?
- ZW-TRANSPOSE-MATRIX-009 A square matrix satisfies A^T=-A (skew-symmetric). What can be said about its main diagonal?