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Niles
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[SOLVED] Finding a basis for a subspace
We have a subspace U in R^3 defined by:
U = {(x_1 , x_2 ; x_3) | x_1 + 2*x_2 + x_3 = 0 }.
Find a basis for U.
We have the following homogeneous system:
(1 2 1 | 0).
From this I find the solution to be written as a*(2,1,0)^T + b(-1,0,1)^T, where a and b are arbitrary constants. From this I find three linearly independant vectors.
Am I correct?
Homework Statement
We have a subspace U in R^3 defined by:
U = {(x_1 , x_2 ; x_3) | x_1 + 2*x_2 + x_3 = 0 }.
Find a basis for U.
The Attempt at a Solution
We have the following homogeneous system:
(1 2 1 | 0).
From this I find the solution to be written as a*(2,1,0)^T + b(-1,0,1)^T, where a and b are arbitrary constants. From this I find three linearly independant vectors.
Am I correct?