Applied Mathematics 1411A/B Chapter 4.7.3: Applied Mathematics 1411A/B Chapter 4.7.: Applied Mathematics 1411A/B Chapter 4.7: Applied Mathematics 1411A/B Chapter 4.: Section 4.7.3

• School: Western University
• Department: Applied Mathematics
• Course: Applied Mathematics 1411A/B
• Professor: Bogdan Tudose

Document Summary

Now, think, when we manipulate a matrix of form ax = 0 with elementary row operations, we omit the collumn of 0"s on the side. This is just how it"s done and we know that through the practice we"ve done. Anyway, it can thus be said that the set of solution vectors is unaffected by performing elementary row operations on the matrix a itself. Thus, if we are not affecting the set of solution vectors, we are thus not affecting the solution space. In this section we have connected the solution space with something called the null space so by association we get the following theorum: Elementary row operations do not change the null space of a matrix. Elementary row operations do not change the row space of a matrix. Elementary row operations do change the column space of a matrix.