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Learn about matrix algebra including inverse matrices, eigenvalues, eigenvectors, diagonal form, and more. Understand concepts, definitions, and applications through detailed examples and exercises.
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Def. Def. 2 x 2 e.g. 3 x 3 e.g. Further Matrix Algebra e.g. In general In general
Res. Further Matrix Algebra Page 142 Exercise 6A
Def. Ex Further Matrix Algebra FP1
Ex Further Matrix Algebra FP1
Transpose of a matrix Ex Page 146 Exercise 6B
FP1 FP1 Inverse Matrices FP1
Ex Inverse Matrices 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.
Def. Matrix of cofactors Inverse Matrices 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.
Ex Inverse Matrices Def.
Ex Inverse Matrices
Inverse Matrices Res. Proof
Inverse Matrices Ex Page 151 Exercise 6C
Range Domain Example Vector Functions Idea The domain or range of a function can have more than one dimension! 1 1 1 2 3 1
Range Domain Example Vector Functions Idea The domain or range of a function can have more than one dimension! 2 2 3 3
? L1 L2 Linear Functions Linear Function Def. L1 L2
Ex Linear Transformations Idea
Linear Transformations Ex Page 159 Exercise 6D
Ex Linear Transformations Idea Don’t find the inverse matrix unless you have to. Page 164 Exercise 6E
Eigenvalues and Eigenvectors Idea There will be some vectors for which the effect of a linear transformation is just like being multiplied by a scalar!
Idea Finding eigenvalues Eigenvalues and Eigenvectors Eigenvectors and Eigenvalues Def.
Idea Normalised vector Def. Eigenvalues and Eigenvectors Characterstic Equation Def.
Eigenvalues and Eigenvectors Ex Page 164 Exercise 6F
Res. Diagonal Form Def. Orthogonal
Diagonalisation Res. Diagonal Form Def. Diagonal Matrix
? Diagonal Form Res.
Diagonal Form Ex Page 186 Exercise 6G
Labels M1 Reference to previous module 1 ? Quick Question Def. Definition Idea Key Idea Ex Example Ex Exercise