Linear Algebra - Can vector $v$ be expressed as a linear combination of $u_1$ and $u_2$ I have a question: Can the vector $v = (1,2)$ be expressed as a linear combination of $u_1 = (1,3)$ and $u_2 = (4,1)$?
What I have tried:
$a + 4b = 1$
$3a + b = 2$
$a = 1 - 4b$
$3(1 - 4b) +b = 2$
$3 - 12b + b = 2$
$3 -11b=2$
$3 -2 = 11b$
$1 = 11b$
$b = 1/11$
$a + 4(1/11) = 1$
$a =1 - 4/11$
$a = 7/11$
Therefore, $v = 7/11x + 1/11y$
That's what I got but I know it's wrong because it doesn't seem right! Any help about how to go about doing this will be much appreciated!

It's correct. You should try with row elimination next as it is much faster, and can be done in fewer steps. 
