MAT 1302 Lecture Notes - Lecture 17: Row And Column Spaces, Free Variables And Bound Variables

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1302
• Professor: Aaron Tikuisis

Document Summary

Subspaces: the subset of another larger vector space. https://ocw. mit. edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-sub spaces/ Null space: the null space of a matrix a is all the solutions. Column space: the column space of a matrix a is the vector space created by all the linear combinations of the columns of a. Important: ax=b is solvable when b is a vector in the column space of a. to the equation ax=0. Basis: the basis for a subspace s of dependent. S is a basis if it isn"t entirely made of zero vectors. Computing the basis of a row: is a set of vectors inside s that spans s and is linearly. 3- the non-zero rows form the basis of row. Important: the rows with leading ones prove that they are linearly independent. Dimension of a subspace: the size of a basis, the bases are finite and 2 bases of the same are linearly independent vectors, then subspace have the same number of vectors.