Topic 2.2 Matrices

This page is, pretty clearly, not even close to being finished.

Lessons

Matrices – basic ideas:

Special matrices, solving matrix equations, using matrices to solve systems of linear equations:

Transformation matrices

There is a nice interactive that illustrates 2D transformations at https://www.geogebra.org/m/vEdEMQRf.

Another nice interactive that illustrates transformations used in computer graphics that incorporate translation as well as the other transformations can be found at https://ncase.me/matrix/. This uses a trick that involves mapping 2D points into 3D so that a 2D translation becomes a 3D shear. (If you’re interested in matrices are used in this context, there’s a ComputerPhile video that may interest you. It has a good representation of the ideas involved,  but beware: the representation of the matrix mathematics is not always strictly correct … look for corrections in the comments.)

Old Matrix content: from the Mathematics Specialist 3D unit

The previous course had Matrices as part of the year 12 Mathematics Specialist course, and covered rather more, including:

1.5 solve systems of up to five simultaneous linear equations with no more than five unknowns, using matrix algebra

1.9 solve practical problems involving the use of Leslie matrices and other examples of transition matrices.

The content below was prepared for the previous course, and is included here for the interest of any students looking for extension material.

Transition matrices

Transition matrices: Markov chains supplement

Leslie Matrices

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