Given that $P = \begin{pmatrix} 2 & -1 \ 4 & 3 \end{pmatrix}$, find the transpose of P, denoted $P^T$.

Question

Accepted Answer

$\begin{pmatrix} 2 & 4 \ -1 & 3 \end{pmatrix}$. The transpose of a matrix is obtained by swapping rows and columns. The first row (2, -1) becomes the first column, and the second row (4, 3) becomes the second column, giving [[2, 4], [-1, 3]]. Option B is the adjugate, C is the original matrix, and D is the negation.

Answer

A) $\begin{pmatrix} 2 & 4 \ -1 & 3 \end{pmatrix}$

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B) $\begin{pmatrix} 3 & 1 \ -4 & 2 \end{pmatrix}$

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C) $\begin{pmatrix} 2 & -1 \ 4 & 3 \end{pmatrix}$

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D) $\begin{pmatrix} -2 & 1 \ -4 & -3 \end{pmatrix}$

Given that $P = \begin{pmatrix} 2 & -1 \\ 4 & 3 \end{pmatrix}$, find the transpose of P, denoted $P^T$.

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