22 lines
624 B
Markdown
22 lines
624 B
Markdown
#rs/class/math163 #math
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- - -
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For a 2 x 2 matrix:
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$$ \det\begin{pmatrix}
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a&b\\c&d
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\end{pmatrix} = \begin{vmatrix} a&b\\c&d\end{vmatrix} = ad-bc$$
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For a 3 x 3 matrix:
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$$\begin{vmatrix} a&b&c\\d&e&f\\g&h&i\end{vmatrix} = a\begin{vmatrix} e&f\\h&i\end{vmatrix} - b\begin{vmatrix} d&f\\g&i\end{vmatrix} + c\begin{vmatrix} d&e\\g&h\end{vmatrix} = a(ei-hf)-b(di-gf)+c(dh-ge)$$
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### Properties
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$$\begin{vmatrix}
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a&b\\a&b
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\end{vmatrix} = ab - ba = 0$$
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$$\begin{vmatrix}
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r\cdot a&b\\r \cdot c&d
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\end{vmatrix} = rad - rbc = r(ad - bc) = r \cdot \begin{vmatrix}
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a&b\\c&d
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\end{vmatrix}$$
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$$\begin{vmatrix}
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1&0\\0&1
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\end{vmatrix} = 1$$
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