(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Span question with Restrictions

**Physics Forums | Science Articles, Homework Help, Discussion**