Matrix Operations

A comprehensive prep sequence for the most challenging questions on the ACT Math and Science sections. It focuses on high-level conceptual blueprints for math topics like complex numbers and matrices, alongside speed-reading and data-interpretation strategies for the Science section.

A comprehensive ACT Math preparation program focusing on essential strategies, high-yield Algebra and Geometry concepts, and realistic practice to boost scores.

This mathematical physics sequence explores the coordinate systems necessary for solving problems involving complex shapes, moving beyond Cartesian coordinates to General Curvilinear systems. Students derive scale factors, volume elements, and differential operators, culminating in solving Laplace's equation and understanding metric tensors.

A graduate-level exploration of expected value applications in finance, covering utility theory, portfolio optimization, risk-neutral pricing, and tail risk metrics. Students transition from theoretical foundations to computational implementation using Monte Carlo methods.

This advanced sequence explores systems of linear equations through the lens of computational linear algebra. Graduate students will move from theoretical existence and uniqueness in vector spaces to matrix factorizations, algorithmic complexity, numerical stability, and iterative methods for large-scale systems.

This sequence explores the geometric interpretation of matrices, treating them as operators that transform space. Students move from calculation to visual application, using matrices to represent coordinates, perform translations/dilations, and apply rotations/reflections via matrix multiplication.

A comprehensive sequence on matrix operations, focusing on determinants, inverses, and their application in solving linear systems and cryptography. Students move from basic calculations to advanced problem-solving techniques.

A comprehensive unit for 10th-grade students exploring matrix operations, from basic dimensions and notation to complex multiplication and real-world applications in inventory management.

A graduate-level sequence exploring the gradient vector as the foundational tool for modern optimization. Students move from the geometric interpretation of multivariate derivatives to the implementation of stochastic algorithms used in machine learning.

This graduate-level sequence explores the distinction between contravariant vectors and covariant co-vectors within the framework of dual spaces, metric tensors, and higher-rank tensor transformations. Students move from rigorous linear algebra definitions to applications in non-Euclidean geometry and physical systems like stress and strain.

This sequence explores matrices as geometric transformations of vectors. Students learn to visualize and calculate how matrices stretch, rotate, reflect, and shear space, culminating in a project where they design a computer graphics animation sequence.

This sequence explores matrix algebra as a tool for data organization and system solving. Students progress from basic arithmetic to complex operations like multiplication, determinants, and inverses, ultimately applying these skills to solve systems of linear equations.

Students will solve systems of linear equations derived from the geometric properties of mutually tangent circles, connecting spatial relationships to algebraic solutions.

A Pre-Calculus lesson on solving 3x3 systems of equations to find quadratic models, featuring a manual elimination method and a matrix inverse method using graphing calculators.

This lesson introduces the Rule of Sarrus as a shortcut for finding 3x3 determinants, comparing its efficiency against the standard cofactor expansion method through a competitive 'Method Battle'.

Students learn to calculate 3x3 determinants using the Cofactor Expansion method, focusing on minor matrices and the checkerboard sign pattern through video analysis and collaborative problem-solving.

A high-school geometry and linear algebra lesson where students use 3x3 matrix determinants to calculate the area of complex, irregular polygons by triangulating coordinate data.

This lesson introduces students to the determinant of 2x2 matrices. Students will learn the calculation formula, practice with various examples, explore matrices with a determinant of zero, and understand the geometric interpretation of a determinant as the area of a parallelogram.

A lesson where 11th-grade students use matrix determinants to calculate the area of geometric figures in the coordinate plane, culminating in a 'Polygon Surveyors' creative application.

Students will bridge the gap between coordinate geometry and linear algebra by connecting the Shoelace Algorithm to matrix determinants. This lesson uses a step-by-step video demonstration followed by algebraic verification of the 3x3 matrix area formula.