09-240/Classnotes for Tuesday December 1: Difference between revisions
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* These are "enough"! |
* These are "enough"! |
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3. <math>det((E_{i,j,c\,\!}A) = det(A) ; |(E^3_{i,j,c\,\!}| = 1 |
3. <math>det((E_{i,j,c\,\!}A) = det(A) ; |(E^3_{i,j,c\,\!}| = 1</math> |
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* Adding a multiple of one row to another does not change the determinant. |
* 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. |
The determinant of any matrix can be calculated using the properties above. |
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<b>Theorem:</b> |
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Revision as of 17:20, 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.
- Adding a multiple of one row to another does not change the determinant.
The determinant of any matrix can be calculated using the properties above.
Theorem:
