Session 22: Using matrices to solve systems of simultaneous linear equations

1. Determinant and inverse of a matrix.
2. Inverse matrices - example.
3. Applications of matrix algebra to simultaneous linear equations.
4. Solving systems of simultaneous linear equations - example 1.
5. Solving systems of simultaneous linear equations - example 2.

• Determinant - theory.
• Determinant - example.
• Inverse matrices - theory.
• Inverse matrices - example.
• Using matrices to solve systems of linear simultaneous equations - theory.
• Using matrices to solve systems of linear simultaneous equations - example 1.
• Using matrices to solve systems of linear simultaneous equations - example 2.

Note that when discussing the role of the determinant in image transformations, we are talking about the absolute value of the determinant. So if for matrix A, -1<det(A)<1 then its effect is area-contracting while if 1<|det(A)| then it is area-expanding.

• Lecture slides.

• Determinants.
• Inverse matrices.