Find Basis of Perpendicular Vectors for v1 & v2

[EvLer]

Homework Statement

how do I find the basis for all vectors that are perpendicular to both
v1 = (1,1,0,0) and
v2 = (1,0,1,1)

If it were 3-D I could find a normal vector via cross product, but in n-dimensions... what do I do?

My one thought is to arrange and solve linear homogeneous system:
[v1][x] = 0
[v2][y] = 0

since RHS is the dot product of the row vector (v1 or v2) and the column [x,y]^t, and for vectors to be perpendicular, their dot product should be 0.
Is that correct?

Thanks in advance.

 

[quasar987]

If I understood correctly and you intend to solve the matrix equation

$$\left( \begin{array}{cccc} 1 & 1 & 0 & 0\\ 1 & 0 & 1 & 1 \end{array} \right)\left( \begin{array}{c} x_1&x_2&x_3&x_4 \end{array}\right)= \left(\begin{array}{c} 0&0 \end{array} \right)$$

then this is what I would do also.