1. The problem statement, all variables and given/known data Let U be the span of [ 0 ] [ 2 ] [ 1 ] and [ 0 ] [ 2 ] [ -1] [ 4 ] [ 1 ] Give conditions on a, b, c and d so that [a b c d] (transposed) is in U (as in, give restrictions that are equations of only a, b, c and d. 2. Relevant equations 3. The attempt at a solution I've set up the problem to set the two given vectors multiplied by scalar x and y, yielding four equations: 2y = a, x = b, 2x - y = c, and 4x + y = d. Is this the right first step to take? After that, I take x or b as a free variable, and try to rewrite the other equations in terms of b, yielding: 2y = a, b = b, 2b - y = c, and 4b + y = d. After this, however, I am stuck. Any pointers? Did I set up the problem the right way? Edit: I also know that [a b c d] must be a linear combination of the two given vectors if it is in the span. However, if it is a linearly independent set, the trivial zero vector could be matched with [a b c d], although I am pretty sure the answer isn't that simple.