MATH 1104 Study Guide - Final Guide: Lincoln Near-Earth Asteroid Research, Row And Column Spaces, London Academy Of Music And Dramatic Art

• School: Carleton University
• Department: Mathematics
• Course: MATH 1104
• Professor: Ayse Alaca

Document Summary

*the vector [x] exists in span if its augmented matrix is consistent. Else, inconsistent means vector [x] is not in the span. Is b in column space of a? if matrix (once ref) is consistent, if consistent then yes, b is in col space of a. Is x in null space of a? if ax = [0] vector, then x is an element of nula. How to find nula: (same as asking for basis of nula: augment with [0] vector such that [a|0, find ref of augmented matrix, solve for x1,x2,x3 > the column space is all solutions to ax=b. > the null space is all solutions to ax=0. How to find a basis for a subspace: put the vectors of the spans as the columns of a matrix, find ref, pivot columns (vectors from original matrix) are in the basis. Definition of basis for a subspace: independent vectors that span the subspace.