Sumários
Valores e vetores próprios
28 Fevereiro 2023, 13:00 • Rita Sousa
[11] (TP)
Valores próprios, vetores próprios e subespaços próprios duma matriz. Exercícios.
5.1(2), ref. 6 da pág. 16 (PUC)
Aula 11
28 Fevereiro 2023, 13:00 • Rita Sousa
Critério de invertibilidade em termos do determinante. Fórmula da adjunta para a inversão de matrizes. Definição de valores e vetores próprios e sua interpretação geométrica.
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28 Fevereiro 2023, 11:00 • Rita Sousa
Determinants: definition, examples. Determinants by cofactor expansion. Arrow technique for 3 by 3 matrices.
Determinants of triangular matrices. Elementary Row Operations and Determinants. Evaluating determinants by row reduction.
Resolution of exercises 5, 6 and 9 from the CUP of week 3.
Lecture 10
28 Fevereiro 2023, 09:30 • Rita Sousa
THEORY
- Further examples of calculating the determinant using Gauss elimination; proof that elementary matrices have non-zero determinant;
- Determinant and matrix operations:
- The determinant of a matrix multiplied by a scalar;
- The determinant ofa matrix sum is not the sum of the determinants of each matrix summand: proof by counter-example;
- The determinant of the transpose matrix;
- The determinant of the matrix product is the product of the determinants of each matrix factor;
- The determinant of the inverse matrix;
- Invertibility criterion for a square matrix in terms of its determinant.
PRACTICE
- The following exercises from CUP - 3rd Week were discussed:
- Ex. 9, 10 and brief overview of the solving strategy for Ex. 12
- The following exercises from CUP - 4th Week were discussed:
- Ex. 1 and 3
BIBLIOGRAPHY
- Week 3:
- Sections 1.6, 4.3, 1.9, 2.1 and 2.5 of Howard Anton, Chris Rorres, Linear Algebra Applications Version, 10th Edition, 2012, Bookman. ISBN: 978854070169
- Week 4:
- Sections 2.3 and 5.1 of Howard Anton, Chris Rorres, Linear Algebra Applications Version, 10th Edition, 2012, Bookman. ISBN: 978854070169