What are the bases for U and W in R^4?

[abcdefg]

let V = R^{4}. Consider the following subspaces:

U = { (a,b,c,d) in R^{4} : a + 2b + 3c = 0, a + b + c + d = 0 }
W = { (a,b,c,d) in R^{4} : a + d = 0, b + c = 0 }

find a basis for U and a basis for W.

i don't even know where to begin. Any help would be very much appreciated. Thanks.

 

[amcavoy]

let V = R^{4}. Consider the following subspaces:

U = { (a,b,c,d) in R^{4} : a + 2b + 3c = 0, a + b + c + d = 0 }
W = { (a,b,c,d) in R^{4} : a + d = 0, b + c = 0 }

find a basis for U and a basis for W.

i don't even know where to begin. Any help would be very much appreciated. Thanks.

Look at the cooresponding matrix and reduce it to row-echelon form. The columns with pivots in them will be the same columns you use for your basis (remember, the same column... but from the ORIGINAL matrix).