(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find (a) a basis for and (b) the dimension of the solution space of the homogeneous system of equations.

x - 2y + z = 0

y - z + w = 0

x - y + w = 0

2. Relevant equations

3. The attempt at a solution

(a)

[1 -2 1 0] => [1 0 -1 2]

[0 1 -1 1] => [0 1 -1 1]

[1 -1 0 1] => [0 0 0 0]

basis = {<1,0,-1,2>, <0,1,-1,1>}

(b) for b i make

x = z - 2w

y = z - w

would i set w = s and z = t?

if so.

[x] = [ t - 2s] = [1] + [-2]

[y] = [ t - s] = t[1] + s[-1]

[z] = [ t ] = [1] + [0]

[w] = [ s ] = [0] + [1]

so the dimension would be the number of vectors

so dimension = 2?

im uncertain about that dimension part

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# Homework Help: Basis and dimension of the solution space

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