### Linear Algebra Calculators: (8) lessons

 [+] Basic m x n Matrix OperationsGiven 2 matrices |A| and |B|, this performs the following basic matrix operations * Matrix Addition |A| + |B| * Matrix Subtraction |A| - |B| * Matrix Multiplication |A| x |B| * Scalar multiplication rA where r is a constant.Features: Calculator | Practice Problem Generator | Watch the VideoTags: addition, matrix, multiplication, operation, scalar, subtraction [+] Cross Product A × BGiven two vectors A and B in R3, this calculates the cross product A × B as well as determine if the two vectors are parallelFeatures: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (3): 8i-j+3k x 5i+j-9k, 6i-3j+6k * 8i+2j-9k, (8i-2j+13k)(3i+5j-k)Tags: cross product, vector [+] Digraph ItemsGiven a digraph, this determines the leader, and symmetric matrix.Features: CalculatorTags: digraph, leader, symmetric [+] Equation of a PlaneGiven three 3-dimensional points, this calculates the equation of a plane that contains those points.Features: Calculator | Practice Problem Generator | Watch the VideoExamples (1): (2,4,6)(1,3,5)(9,8,4)Tags: equation, plane [+] Markov ChainGiven a transition matrix and initial state vector, this runs a Markov Chain process.Features: Calculator [+] Matrix PropertiesGiven a matrix |A|, this calculates the following items if they exist: * Determinant = det(A) * Inverse = A-1 * Transpose = AT * Adjoint = adj(A) * Eigen equation (characteristic polynomial) = det|λI - A| * Trace = tr(A) * Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form * Dimensions of |A| m x n * Order of a matrix * Euclidean Norm ||A|| * Magic Sum if it exists * Determines if |A| is an Exchange MatrixFeatures: Calculator | Practice Problem Generator | Watch the VideoTags: adjoint, determinant, dimension, echelon, eigen, inverse, matrix, norm, polynomial, transpose [+] Plane and Parametric Equations in R3Given a vector A and a point (x,y,z), this will calculate the following items: 1) Plane Equation passing through (x,y,z) perpendicular to A 2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A Features: Calculator | Watch the VideoTags: parametric, plane, vector [+] VectorsGiven 2 vectors A and B, this calculates: * Length (magnitude) of A = ||A|| * Length (magnitude) of B = ||B|| * Sum of A and B = A + B (addition) * Difference of A and B = A - B (subtraction) * Dot Product of vectors A and B = A x BA ÷ B (division) * Distance between A and B = AB * Angle between A and B = θ * Unit Vector U of A. * Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes). * Cauchy-Schwarz Inequality * The orthogonal projection of A on to B, projBA and and the vector component of A orthogonal to B → A - projBA Also calculates the horizontal component and vertical component of a 2-D vector.Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (4): {1,2,3} + {4,5,6}, {2,4,6,8,10} + {1,3,5,7,9}, {9,8,7,6} x {4,3,2,1), {12,9,6} / {4,3,2}Tags: angle, cosine, direction, inequality, magnitude, orthogonal, orthogonal, perpendicular, product, projection, vector