Core linear algebra tools for further study in engineering, CS, and data science.
~ 6–8 hours, 3 lessons, 20+ practice tasks
Algebra, functions, vectors, basic geometry
Compute inverses, solve systems, interpret linear maps
Matrix arithmetic, 2×2 determinant and inverse, solving Ax=b.
Augmented matrices, elimination, rank, solution structure, and span.
Bases, dimension, linear transformations and matrices, geometric view.
Why doesn't matrix multiplication satisfy commutativity?
Because the order of linear combinations of columns and rows differs, representing different transformation compositions, usually AB ≠ BA.
How to intuitively understand determinants?
In 2D it's an area scaling factor, in 3D it's a volume scaling factor; when 0, it means flattening to lower dimensions.