MATH136 Study Guide - Final Guide: Scalar Multiplication, Euclidean Vector, Linear Independence

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: knjnl

Document Summary

Summary of the most fundamental topics in the math 136 w14. Vectors in rn, vector addition and scalar multiplication, dot products, cross. Subspace of rn, linear independence of a set, span of a set, basis of a products. subspace. Angle between vectors in rn, norm of a vector, orthogonal vectors, orthogonal set, orthonormal set. Scalar equation of a plane, vector equation of a plane, normal to a plane. Projection of a vector (point) onto a line, projection of a vector (point) onto a plane, projuv, perpuv, Systems of linear equations, homogeneous systems, solutions in the form of a vector equation, elementary row operations, row equivalence, rref, Matrix algebra, transpose, matrix-vector multiplication, identity matrix, inverse of a matrix, matrix decomposition to elementary matrices, similar matrices, matrix equations. Linear mappings rn to rm, rotation, reflection, standard matrix of a linear map, ker(l), operations on linear maps. Rank, nullspace, row space, column space of a matrix.