# Linear Algebra Subspaces Basis

## Homework Statement

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.

none really

## 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

Evo
Mentor

## Homework Statement

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.

none really

## 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
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.

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

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

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

U∩W = (v_2)

please i need to this quickly

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

U∩W = (v_2)

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.

please i need to this quickly

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

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

berkeman
Mentor
please i need to this quickly

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