Originally Posted by

**Deadstar** Can someone explain how to get this answer please.

Let $\displaystyle U_1$ and $\displaystyle U_2$ be the subspaces of $\displaystyle R^4$ defined by

$\displaystyle U_1 = (x = (x_1,x_2,x_3,x_4)|x_1 + 2x_2 - x_3 - x_4 = 0)$

and

$\displaystyle U_2 = (x = (x_1,x_2,x_3,x_4)|x_1 - x_2 + x_3 + x_4 = 0)$

Find basis for $\displaystyle U_1 $ and $\displaystyle U_2 $ and $\displaystyle U_1 \cap U_2$

Now i can find basis for $\displaystyle U_1 $ and $\displaystyle U_2$ fairly easily tho they were different from the ones given in the solutions. Problem is i have no idea how to calculate $\displaystyle U_1 \cap U_2$. This is the solution given.

(-2, 1, 0, 0), (1, 0, 1, 0) and (1, 0, 0, 1) form a basis for $\displaystyle U_1$

(1, 1, 0, 0), (-1, 0, 1, 0) and (-1, 0, 0, 1) form a basis for $\displaystyle U_2$

(-1, 2, 3, 0), (-1, 2, 0, 3) form a basis for $\displaystyle U_1 \cap U_2$

can someone explain this?