Flashcards
Matrices: Inverse & Determinants
Cards in this deck (10)
- 1Existence of the inverse
- 2Solving linear systems via the inverse
- 3n x n determinant: geometric interpretationn-dimensional volume of the n-dimensional counterpart of a parallelogram spanned by the row vectors of the matrix
- 4Universal laws of swaps1. It is always possible to turn any permutation of the first n numbers into the identity permutation 1234…n using swaps
2. For any given permutation, the different ways to turn it into the identity permutation either all involve an even or all involve an odd number of swaps - 5Multiplying A by an arbitrary number, aEvery element of A gets multiplied by a, and there are n factors in each term of the determinant
- 6Elementary matrix: swapping rowsOdd permutation => determinant = -1
- 7Elementary matrix: multiply a row by a number, a
- 8Elementary matrix: add a multiple of one row to another row
- 9Non-zero determinant: equivalences
- 10Cramer's rule
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- Mathematics Flashcards on Matrices: Inverse & Determinants, created by Melina Mackey on 06/06/2019.
- Created by
- Melina Mackey · Jun 2019
- Updated
- Jun 6, 2019
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- Created by Melina Mackey · Apr 20, 2019
- Copied by Melina Mackey · Apr 21, 2019
- Copied by Melina Mackey · Jun 1, 2019
- Copied by Melina Mackey · Jun 6, 2019
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