Find all values of h such that the vectors {a1, a2, a3} span r3, where a1 = ? 1 h 7 , a2 = 4 ? 2 5 , a3 = 1 ? 7 2 .

Assuming you wrote





will span provided that they comprise a set of linearly independent vectors. This happens when the only solution to the following is :




There will be a non-zero solution whenever is singular, i.e. when . You have



which has a solution of . This is the only value that makes the set of vectors linearly dependent, which means all guarantee that span all of .