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Linear Algebra and Analytic Geometry

Course Description: Introduction to conic sections, the parabola; displacement of coordinate axes, the ellipse, the hyperbola, rotation of axes; the quadratic equation. Systems of linear equations and matrices: introduction, Gaussian elimination, matrices and their operations, inverses; rules of matrix algebra, elementary matrices and a method for finding A-1, additional results about systems of equations and invertibility, diagonal, triangular, and symmetric matrices. Determinants: determinants using cofactor expansion, computing determinants using row reduction, properties of the determinant function, a combinatorial introduction to determinants. Vectors in two and three dimensions: introduction to vectors, vector norms; computing vectors, the dot product, lines and planes in three dimensions.
Credit hours: 3
Objectives of the course :

Demonstrate proficiency in engineering and algebraic curricula for developing concepts and solving problems using fundamental algebraic techniques.

Formulating systems of linear equations, which are widely used in various engineering applications, finding solutions if they exist, and interpreting the results meaningfully.

(C) Using matrices, determinants, and their operations.

(D) Use vectors and their analysis to solve problems involving two and three dimensions.

(E) Finding the equations of lines and planes in three dimensions and using them to determine their relative positions and intersections.

Course outputs :

Define the concept of a conic section.
2. Define a system of linear equations.

3. Describe the basic concepts and characteristics of matrices.
4. Describe the fundamental properties of determinants and their decomposition.

5. Describe the fundamental concepts and properties of vectors in two-dimensional spaces.

6. Three-dimensional spaces and multi-dimensional spaces.

7. Draw the conic sections: parabola, ellipse, and hyperbola.

8. Solve the system of linear equations.
9. Calculate the angle and orthogonality in an inner product space. Evaluate the eigenvalues and eigenvectors of the matrix.

Additional information:
  • Last updated: 2026-05-17

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