# Linear Algebra Subspaces Basis

1. Oct 5, 2011

### bob258173498

1. The problem statement, all variables and given/known data

a) If U and W are subspaces of R^3, show that it is possible to find a basis B for R^3 such that one subset of B is a basis for U and another subset of B (possibly overlapping) is a basis for W.

b) If U and W are subspaces of a finite-dimensional vector space V, show that it is possible to find a basis for V such that one subset of that basis is a basis for U and another subset of that basis (possibly overlapping) is a basis for W.

2. Relevant equations

none really

3. The attempt at a solution

B = ( v_1, v_2, v_3 ), such that these vectors are a basis for V.

Then:

V = t_1*v_1 + t_2*v_2 + t_3*v_3

...stuck here

2. Oct 5, 2011

3. Oct 5, 2011

4. Oct 5, 2011

### Staff: Mentor

People will help if they wish. They probably will not help you since you keep bumping your thread every few minutes, which is against the rules.

5. Oct 5, 2011

### bob258173498

V = (v_1, v_2, v_3)
U = ??? it never told us

Please can someone help.

6. Oct 5, 2011

### bob258173498

Guys please, I'm begging you

7. Oct 5, 2011

### micromass

Staff Emeritus
Start off by finding a basis for $U\cap W$.

8. Oct 5, 2011

### bob258173498

U = (v_1, v_2)
W = (v_2, v_3)

U∩W = (v_2)

9. Oct 5, 2011

### bob258173498

please i need to this quickly

10. Oct 5, 2011

### micromass

Staff Emeritus
No, what makes you think that U and W are two-dimensional?? U and W can be anything!!

First construct a basis for $U\cap W$, then extend this basis to a basis of U and extend it to a basis of W.

Messages like this actually incline people to help you less. Just so you know.

11. Oct 5, 2011

### Staff: Mentor

24 hour time out due to ignoring the rules, ignoring the warning and continuing to bump.

12. Oct 6, 2011

### Staff: Mentor

Do you need it quickly because it is part of a midterm exam?