09-240/Classnotes for Tuesday December 1: Difference between revisions
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MAT240 – December 1st |
MAT240 – December 1st |
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Basic Properties of det: M<sub>nxn</sub> |
Basic Properties of det: M<sub>nxn</sub>→F: 0 det(I) = 1 |
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1. <math>det(E'_{i,j\,\!}A) = -det(A) ; |E'_{i,j\,\!}|= -1. [Note: det(EA) = |E||A|]</math> |
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* Also, note that exchanging two rows flips the sign. |
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2. <math>det(E^2_{i,c\,\!}A) = det(A) ; |(E^2_{i,j,c\,\!}| = 1</math> |
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* These are "enough"! |
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3. <math>det((E_{i,j,c\,\!}A) = det(A) ; |(E^3_{i,j,c\,\!}| = 1 |
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* Adding a multiple of one row to another does not change the determinant. |
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The determinant of any matrix can be calculated using the properties above.</math> |
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Revision as of 16:19, 1 December 2009
--- Wiki Format ---
MAT240 – December 1st
Basic Properties of det: Mnxn→F: 0 det(I) = 1
1.
![{\displaystyle det(E'_{i,j\,\!}A)=-det(A);|E'_{i,j\,\!}|=-1.[Note:det(EA)=|E||A|]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93b201c57138463bb97bc0ea059970a95c7d0fd0)
- Also, note that exchanging two rows flips the sign.
2.
- These are "enough"!
3.
