You need to solve:

.... (1)

.... (2)

Since there are an infinite number of solutions and you only needamatrix, let c = 0.

Then

.... (1')

.... (2')

A solution to (1') and (2') is and .

So the elements of the second row in the matrix are , , 0.

To get the elements of the third row, you could construct a unit vector normal to (1, 2, 2) and (-2, 1, 0) and use its components .....

For checking purposes, I get , , .