Status: Tags: #cards/math232/unit5 Links: Matrix
Determinants
Principles
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- Help determine if a matrix is invertible
- Can do matrix operations on rows + columns to help simplify !
Determinant of a matrix with a row/column with 0s ? 0
Determinant of an upper/lower triangular matrix ? Product of diagonal entries of A
- $det A = a_{11}a_{22}…a_{nn}
Deterimant of
Types
Determinant of 2x2 matrix ?
- ad-bc
- if = 0, then invertible
Determinant of a 3x3 matrix (matrix form)
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- Only invertible if != 0
Determinant of a 3x3 matrix ? $a_{11}C_{11} + a_{12}+C_{12} + a_{13}C_{13}$
- Where C are cofactors
Determinant of an nxn matrix (fixed r/c)
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Determinant of nxn matrix (free r/c)
Examples
3x3
Calculate det $\begin{bmatrix}
1 & 2 & 3 \\-2 & 2 & 1 \\5 & 0 & 1
\end{bmatrix}$
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nxn
Calculate
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References:
Created:: 2022-03-02 15:52