Let A=\begin{bmatrix}a&b\\c&d\end{bmatrix} and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA''

Let A=\begin{bmatrix}a&b\\c&d\end{bmatrix} and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA''

Question
Vectors and spaces
asked 2021-03-12

Let \(\displaystyle A=\begin{bmatrix}a&b\\c&d\end{bmatrix}\) and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA''

Answers (1)

2021-03-13

Given \(\displaystyle A=\begin{bmatrix}a&b\\c&d\end{bmatrix}\)
So \(\displaystyle kA=\begin{bmatrix}ka&kb\\kc&kd\end{bmatrix}\)
now \(\displaystyle det(kA)=\begin{vmatrix}ka&kb\\kc&kd\end{vmatrix}=k^2\begin{vmatrix}a & b \\c & d \end{vmatrix}\)
\(\displaystyle{\det{{\left({k}{A}\right)}}}={k}^{{2}}\ {\det{{\left({A}\right)}}}\)

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