1 Vectors
A vector has magnitude and direction, written as components [x, y, z]. Add componentwise; scale by a scalar. The dot product a·b = Σ aᵢbᵢ measures alignment and gives the angle between vectors.
Linear Algebra Intermediate
Vectors, matrices and transformations — the language of graphics, ML and engineering systems.
📚 Lessons
2 Matrices
A matrix is a rectangular array of numbers. Matrix multiplication combines transformations; it is associative but not commutative. The identity matrix I leaves vectors unchanged.
3 Linear systems
Systems Ax = b are solved by Gaussian elimination or by the inverse x = A⁻¹b when A is invertible. The determinant indicates invertibility (zero → singular) and scales area/volume.
4 Eigenvalues & applications
Eigenvectors keep their direction under a transformation, scaled by an eigenvalue: Av = λv. They power PCA, vibration analysis, PageRank and stability analysis. Linear algebra also drives 3D graphics and machine-learning models.
📝 Tasks
7 tasks across 3 pages — multiple-choice and fill-in (type the answer). Score 70% or higher to earn your certificate.
🎓 Certificate of Completion
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