ЭШ · Суралцах · 70 бодлого
Vectors & Matrices Вектор ба матриц
Vector arithmetic and coordinates, the dot product, 3D vectors, then matrix operations, determinants and inverses, geometric transformations as matrices, and systems in three unknowns — the exam connects vectors to geometry and matrices to systems.
Сургалтын хөтөлбөр (БСШУСЯ, А/492): 10.4, 10.9, 10.11, 11.2, 11.8
01 · Курс
8 нэгжээс 8 нь бэлэн — хичээл, дадлага, өөрийгөө шалгах тесттэй. Хичээлүүд одоогоор англи хэлээр; монгол орчуулга дараа нэмэгдэнэ.
01 Vector Arithmetic Adding tip-to-tail, scaling, subtracting, vectors inside triangles and parallelograms, and the section formula. Start 02 Vectors & Coordinates What a vector is, components and magnitude, equal/opposite/parallel vectors, and unit vectors — arrows made of numbers. Start 03 The Dot Product Multiply vectors into a number: computing u·v, reading angles from its sign, perpendicularity tests, and the |u+v|² expansion toolbox. Start 04 Vectors in Space The third coordinate: 3D magnitude, arithmetic and dot products in space, the box diagonal, and normal vectors of planes. Start 05 Matrices & Operations Number grids and their arithmetic: entries and dimensions, adding and scaling, and the row-times-column multiplication that runs everything. Start 06 Determinants, Inverses & Systems The determinant ad − bc, the 2×2 inverse, solving systems with matrices and Cramer's rule, and matrices as transformations — the capstone. Start 07 Transformation Matrices Every geometric transformation as four numbers: reflections, rotations, enlargements, the translation that needs a third coordinate, and how to compose and name them. Start 08 Systems in Three Unknowns Elimination with the letters removed: augmented matrices and row operations, Gauss's method, the 3x3 determinant and inverse, and Cramer's rule for three unknowns. Start