1. The problem statement, all variables and given/known data Let S be the subspace of all vectors in R4 that are orthogonal to each of the vectors (0, 4, 4, 2), (3, 4, -2, -4) What is an example of a matrix for which S is the nullspace? 3. The attempt at a solution I'm not sure how I should be intepreting the question: [ 0 ,4 ,4 ,2 ;3, 4, -2, -4] = [ x , y ,z , t] = [ 0 , 0 ] 0x + 4y + 4z + 2t = 0 3x + 4y -2 z -4t = 0 from here I set up an augmented matrix and solve for the set of vectors x ,y ,z ,t? By definition if x, y, z, t results in each linear equation = 0, then, x ,y ,z ,t are vectors with properties of orthogonality?