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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.

The Student and Tutor reviewed the formula and methodology for calculating determinants of 3x3 matrices, including the sign convention for co-factors. The Student practiced several determinant problems and discussed a personal visualization technique for matrix elements. The plan for future sessions includes practicing more determinant questions, followed by co-factors, transpose, and inverse matrices.

The Tutor and Student worked through solving systems of linear equations using the invertible matrix method. They practiced identifying matrices A, X, and B, calculating the determinant and adjugate of matrix A, and finally multiplying the inverse of A by B to find the solution. The Student was advised to practice calculating determinants and cofactors separately.

The Tutor and Student reviewed quadratic equations and then focused on solving systems of linear equations using the matrix inverse method. They practiced converting systems into matrix form, calculating determinants, cofactors, adjugates, and inverses for both 2x2 and 3x3 matrices, and then applied these to find the variable matrices. The next session will involve creating and solving 3x3 systems of equations.