1. Further Matrix Algebra
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Def.
e.g.
Def.
e.g.
2 x 2
In general
e.g.
3 x 3
In general

2. Transpose of a matrix
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3. Transpose of a matrix
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4. Transpose of a matrix
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5. Further Matrix Algebra
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Res.
Page 142
Exercise 6A

6. Further Matrix Algebra
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FP1
Def. Ex

7. Further Matrix Algebra
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FP1 Ex

8. Transpose of a matrix
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9. Transpose of a matrix
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Page 146
Exercise 6B

10. Inverse Matrices
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FP1
FP1
FP1

11. Ex Inverse Matrices Minor Def.
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Def.
Minor
The minor of an element is the determinant of the elements which remain when the row and column containing the element are crossed out. Ex

12. Inverse Matrices Matrix of minors Def.
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Def.
Matrix of minors
The matrix of minors M of a matrix A is found by replacing each element of A with the minor of that element.
Def.
Matrix of cofactors

13. Inverse Matrices
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Def. Ex

14. Inverse Matrices
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15. Inverse Matrices
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Res.
Proof

16. Inverse Matrices
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Page 151
Exercise 6C

17. The domain or range of a function can have more than one dimension!
Vector Functions
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Idea
The domain or range of a function can have more than one dimension!
Domain
Range
Example
1 1
1 2
3 1

18. The domain or range of a function can have more than one dimension!
Vector Functions
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Idea
The domain or range of a function can have more than one dimension!
Domain
Range
Example
2 2
3 3

19. Linear Functions
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Linear Function
Def. L1 L2 ? L1 L2

20. Linear Transformations
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Idea Ex

21. Linear Transformations
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22. Linear Transformations
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23. Linear Transformations
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24. Linear Transformations
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Page 159
Exercise 6D

25. Linear Transformations
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26. Linear Transformations
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27. Linear Transformations
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Idea
Don’t find the inverse matrix unless you have to. Ex
Page 164
Exercise 6E

28. Eigenvalues and Eigenvectors
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Idea
There will be some vectors for which the effect of a linear transformation is just like being multiplied by a scalar!

29. Eigenvalues and Eigenvectors
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Eigenvectors and Eigenvalues
Def.
Idea
Finding eigenvalues

30. Eigenvalues and Eigenvectors
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Characterstic Equation
Def.
Idea
Def.
Normalised vector

31. Eigenvalues and Eigenvectors
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32. Eigenvalues and Eigenvectors
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33. Eigenvalues and Eigenvectors
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34. Eigenvalues and Eigenvectors
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35. Eigenvalues and Eigenvectors
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Page 164
Exercise 6F

36. Diagonal Form
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Def.
Orthogonal
Res.

37. Diagonal Form Def. Res. Diagonal Matrix Diagonalisation
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Def.
Diagonal Matrix
Res.
Diagonalisation

38. Diagonal Form
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Res. ?

39. Diagonal Form
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40. Diagonal Form
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41. Diagonal Form
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42. Diagonal Form
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Page 186
Exercise 6G

43. ? M1 Labels Ex Ex Def. Idea Reference to previous module 1
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Reference to previous module 1 ?
Quick Question
Def.
Definition
Idea
Key Idea Ex
Example Ex
Exercise