Given that \(P = \begin{pmatrix} 4 & 9 \end{pmatrix}\) and \(Q = \begin{pmatrix} -1 & -2 \\ 3 & 2 \end{pmatrix}\). Evaluate \(|Q|P\).
Question 1 Report
Given that \(P = \begin{pmatrix} 4 & 9 \end{pmatrix}\) and \(Q = \begin{pmatrix} -1 & -2 \\ 3 & 2 \end{pmatrix}\). Evaluate \(|Q|P\).
Answer Details
To evaluate \(|Q|P\), we first need to calculate the determinant of matrix \(Q\), denoted as \(|Q|\).
$$
\begin{aligned}
|Q| &= \begin{vmatrix} -1 & -2 \\ 3 & 2 \end{vmatrix} \\
&= (-1\times2) - (-2\times3) \\
&= -2 + 6 \\
&= 4
\end{aligned}
$$
Next, we multiply the matrix \(P\) by the determinant of matrix \(Q\).
$$
\begin{aligned}
|Q|P &= 4\begin{pmatrix} 4 & 9 \end{pmatrix} \\
&= \begin{pmatrix} 16 & 36 \end{pmatrix}
\end{aligned}
$$
Therefore, the answer is \(\begin{pmatrix} 16 & 36 \end{pmatrix}\).
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