MATH 1107 Lecture : Lesson 16b - Important Spaces.pdf

• School: Carleton University
• Department: Mathematics
• Course: MATH 1107
• Professor: all

Document Summary

This means that as long as b is in the span{c1, c2, cn} . thi th t bi ti l i li. This tells us which x makes ax = 0 hi h i f th t t fi di i d th ll. Proof: note that for both matrices to have the same row space, both matrices. = c (r x) + c (r x) + If we want to prove that two matrices have the same kernel, we simply do the following: row reduce a and b to rref, as long as they have the same rref matrix (with the exception of zero rows) they both will have the same kernel. (and thus have the same row space as well). Setting up our new matrix system and row reducing gives: This means we have: x5=t1 (free) x4=t2 (free) x3=t3 (free) x2=2t2 t3 x1=t2 t3.