CONTENTS

1. Matrices

Definition and representation.

Square and rectangular matrices.

Equality of matrices.

Transpose of a matrix and symmetric matrix.

Matrix operations.

Properties.

Elementary row and columns operations.

Matrices equivalency.

Condensation of a matrix.

Rank of a matrix.

Gauss Elimination's Method (GEM).

Inverse of a matrix; computation using GEM.

2. Determinants

Definition.

Evaluating 2nd and 3rd order determinants by Sarrus' Rule.

Laplace's Theorem.Evaluating determinants of any finite order.

Properties.

3. Systems of linear equations

Definition.

Matrix notation.

Homogeneous systems.

The Cramer's Rule.

Resolution by Gaussian Elimination Method.

4. Real vector spaces

Definition and properties.

Subspaces.

Linear combinations.

Set of generators.

Linear dependence and independence of vectors.

Basis and dimension.

5. Linear transformations

Definition and properties.

Matrix of a linear transformation

Kernel and image.

Eigenvalues and eigenvectors.

6. Analytical Geometry

Cross product and dot product of two vectors.

Equations of line and plane.

Intersections of lines and planes.

Relative positions of lines.

Angles between geometrical identities.