johnniesha226 johnniesha226
  • 14-04-2020
  • Mathematics
contestada

Find the determinancof the matrix Q.

Find the determinancof the matrix Q class=

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LammettHash
LammettHash LammettHash
  • 14-04-2020

Using a Laplace expansion along the first column, we have

[tex]\det Q=2\det\begin{bmatrix}2&1\\-1&6\end{bmatrix}+3\det\begin{bmatrix}3&4\\-1&6\end{bmatrix}+5\det\begin{bmatrix}3&4\\2&1\end{bmatrix}[/tex]

The determinant of a 2x2 matrix is trivial,

[tex]\det\begin{bmatrix}a&b\\c&d\end{bmatrix}=ad-bc[/tex]

So we have

[tex]\det Q=2\cdot13+3\cdot22+5\cdot(-5)=67[/tex]

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