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?
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?