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 :(

re: Gaussian elimination help II

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

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?

ADDENDUM://

once when you get used to setting up the system of linear equations like this, you can 'shortcut' and insert the spanning vectors as column vectors (in any order) with the 'solution' vector as the last column vector for the desired matrix to solve.