Chapter 2 Question 12 / Help

[matthias-herrmann]

For my understanding: The Intersection of U1 and U2 has only one independent column. Let's call the combination of the matrices V. Therefore av1+...av6 can be reduced by a singel linear combination a*v?

I understand that because dim(U1)=2 and dim(U2) we can set 0=a1v1+a2v2-a4v4-a5v5

Then the solution says v1,v2,v4 are linearly independent and we can set a5 to any number e.g. 9.

How does the augmented matrix look like to solve for v?

                                         | a1
                           ?            | a2
                                         | a4
                                         | 9