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The Tutor and Student worked on solving quadratic equations without a constant term, demonstrating the factoring process. They then progressed to finding the eigenvalues of a 3x3 matrix, which involved calculating its determinant to derive a cubic characteristic equation, followed by using polynomial long division and factorization to find its roots. The Tutor was advised to review the solution after class.

The Student and Tutor reviewed the process of finding eigenvalues for 2x2 matrices. They practiced using the formula `det(A - λI) = 0` to derive quadratic equations, which were then solved using both the quadratic formula and the product sum (middle term split) factorization method. Homework on quadratic equations was planned for further practice.

The Student and Tutor reviewed the process of finding the inverse of a matrix to solve systems of linear equations, practicing calculations for co-factors, adjoints, and determinants. The session then introduced the new academic concept of eigenvalues and eigenvectors, including their fundamental equation and characteristic equation. They worked through a 2x2 matrix example to calculate eigenvalues, and the Student will review this new concept for the next class.

The Student and Tutor reviewed the process of finding matrix co-factors and the adjoint matrix for solving systems of linear equations using the inverse matrix method. The Student practiced calculating co-factors for a 3x3 matrix and discussed common calculation errors. Two practice problems on matrix inversion were assigned as homework, and the next session will focus on values and vectors.

The session focused on practicing essential matrix operations, with the Student and Tutor reviewing and working through problems on determinants and co-factors of 3x3 matrices. The Student practiced calculations for two different matrices, identifying and correcting errors related to handling negative signs. They also briefly touched upon adjoint matrices, with plans to cover invertible matrices in the upcoming class and the Tutor offering supplementary practice worksheets.

The Student and Tutor focused on solving a geometry problem involving a cylinder inscribed in a sphere, deriving formulas for its surface area and volume using trigonometric relationships. They practiced substituting these derivations into complex expressions and simplifying them. The session ended with the introduction of a compound interest problem.