Hello. First, I'd like to apologize because I don't know where to go ask for homework on linear algebra on the forums so if anyone could please let me know, that would be appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

Here's the question:Find a basis for the subspace of R^4 spanned by the given vectors

Here's the answer at the end of the textbook:

so the matrix A is

( 2 4 -2 3)

(-2 -2 2 -4)

(1 3 -1 1)

and the book puts it in reduced row echelon form which comes out to

( 1 0 -1 5/2 )

( 0 1 0 -1/2)

(0 0 0 0 )

Thus a basis for the subspace is { (1, 0, -1, 5/2), (0, 1, 0, -1/2) }

My question is:

Is this the only answer you can get or can I get different answers.

Say, if I used paramters "a" and "b" for column x3 and x4 respectively, then I can get

x1 = a - (5/2)b

x2 = (1/2)b

x3 = a

x4 = b

then if I let a = 0 and b =1, I'd get:

(-5/2, 1/2, 0, 1)

then if I let a = 1 and b = 0, I'd get:

(1, 0, 1, 0)

thus a basis for the subspace is { (-5/2, 1/2, 0, 1), (1, 0, 1, 0) }

Could that be another answer?

Also, I thought for it to be a basis, it has to be linearly independent. Are they assuming that by inspection it's linearly independent so that's why the book isn't testing for independence?

Thank you so much for any guidance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Find a basis for the subspace of R^4 spanned by the given vectors (attempt inside)

**Physics Forums | Science Articles, Homework Help, Discussion**