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Systems of linear equations and solutions, Gauss-Jordan Elimination (Elementary Line Operations), matrix and matrix operations, matrix ratios, matrix operation properties;
Inverse matrix, elementary matrix and inverse search method matrix;
Types of matrices, Determinants: counting determinants using line reduction, Determinant Properties, Cofactor Expansion, Cramer Rules. Vectors in the Euclid Chamber, vector operation, norm, distance of two vectors, point product, projection, cross product in R3;
The linear transformation of the Euclid Space, the properties of linear transformations;
Subspaces, linear combinations, linearly independent, linearly independent, vector builders, bases, dimensions, eigenvalues, eigenvectors, characteristic spaces, diagonalizations.

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