1. Does the set S SPAN R3 ?

2. Does the set S SPAN R3 ?
Is every vector in R3 a linear combination
of the vectors in S?
For every vector in R3 can you find scalars?

3. Does the set S SPAN R3 ?
Is every vector in R3 a linear combination
of the vectors in S?

4. Does the set S SPAN R3 ?
Is every vector in R3 a linear combination
of the vectors in S?

5. Does the set S SPAN R3 ?
Is every vector in R3 a linear combination
of the vectors in S?

6. Does the set S SPAN R3 ?
Suppose x = 5, y = 3, z = 4

7. Does the set S SPAN R3 ?
Suppose x = 5, y = 3, z = 4 5 5 5 5

8. Does the set S SPAN R3 ?
Suppose x = 5, y = 3, z = 4 5 3 5 3 3 5 5

9. Does the set S SPAN R3 ?
Suppose x = 5, y = 3, z = 4 5 3 4 5 3 4 3 5 4 5

10. Does the set S SPAN R3 ?
Suppose x = 5, y = 3, z = 4 5 3 4 5 3 =2 4 =4 3 5
=-1 4 5

11. Does the set S SPAN R3 ?
Suppose x = 5, y = 3, z = 4 5 2 4 -1
check 3 4 5 3 =2 4 =4 3 5
=-1 4 5

12. Does the set S SPAN R3 ?
Whatever you substitute for
x, y and z, you will be able to
find c1 , c2 , and c3