Homework SourseB 1 1 1 1 1 0 0 1 0 0 0 1 Determine a basis for B SolutionL
B = {[1 1 1 1], [1 0 0 1], [0 0 0 1]} Determine a basis for B ![B = {[1 1 1 1], [1 0 0 1], [0 0 0 1]} Determine a basis for B SolutionLet, x=[a b c d]^T be in B perpendicular Taking dot product for vectors in B gives a+b+c+](/WebImages/16/b-1-1-1-1-1-0-0-1-0-0-0-1-determine-a-basis-for-b-solutionl-1026258-1761531388-0.webp "B = {[1 1 1 1], [1 0 0 1], [0 0 0 1]} Determine a basis for B SolutionLet, x=[a b c d]^T be in B perpendicular Taking dot product for vectors in B gives a+b+c+")
Solution
Let, x=[a b c d]^T be in B perpendicular
Taking dot product for vectors in B gives
a+b+c+d=0
a+d=0
d=0
Hence, a=0
b+c=0
b=-c
x=b[0 -1 1 0]^T
This is basis for B perpendicular : {[0 -1 1 0]^T}
