Homework SourseGiven the same matrix A 9 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 Is t
Given the same matrix A= [9 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0] Is the vector v = [[2 1 -1 - 1]^T a member of its row space? Show why or why not.![Given the same matrix A= [9 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0] Is the vector v = [[2 1 -1 - 1]^T a member of its row space? Show why or why not.SolutionNo it is no](/WebImages/16/given-the-same-matrix-a-9-0-1-0-0-0-1-0-1-1-1-1-0-0-1-0-is-t-1025985-1761531214-0.webp "Given the same matrix A= [9 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0] Is the vector v = [[2 1 -1 - 1]^T a member of its row space? Show why or why not.SolutionNo it is no")
Solution
No it is not.
For the given vector the second column entry is 1 and 4th column entry is -1
Now let us look at individual rows of matrix A.
There is only one row with non zero entries in 2nd and 4th column which is the 3rd row and the entries in 2nd and 4th column respectively are 1 and 1. Hence any multiple of this row will always give equal values in 2nd and 4th column.
HEnce proved
