# Thread: Gaussian elimination help II

1. ## Gaussian elimination help II

1.Are the vectors
(-1,3,1) and (-1,4,1) in the span of {[1,0,1],[1,2,2],[0,4,2]}?

2. Calculate AB and BA if possible. If not, explain why.

A=1 0 2 B= 0 -1 1 2
-1 -3 0 1 0 2 3
-3 -1 0 0

How would you solve these two questions? Can someone tell me how to do this problem and how to solve it? Please and thanks in advance

2. ## re: Gaussian elimination help II

Can anyone help me with number 1, i managed to solve number 2.

3. ## re: Gaussian elimination help II

In order to solve 1, you can first set up a system of linear equations.
For example, if [-1,3,1] is in the span{[1,0,1] , [1,2,2] , [0,4,2]}, then by definition there exists scalar multiples x,y,z such that

[1,0,1] x + [1,2,2] y + [0,4,2] z = [-1,3,1]
combining each of these vectors using addition and multiplication yields

[x+y, 2y+4z, x+2y+2z] = [-1, 3, 1]
Hence by comparison

x+y= -1
2y+4z = 3
x + 2y + 2z = 1

You can solve this system using a matrix or by substitution. (if there is no such x,y,z then we know it's not in the span) can you take it from here?