Question: Consider the linear system ( 2x1 + 2x2 + 3x3 3x4 + x5 = 4 x1 + 4x2 + 2x3 + 2x4 + 3x5

Consider the linear system ( 2x1 + 2x2 + 3x3 − 3x4 + x5 = 4 x1 + 4x2 + 2x3 + 2x4 + 3x5 = 5 For this system, do the below:

(a) (5 points) Show it is compatible (or consistent)

(b) (10 points) Find all solutions xh of the associated homogeneous linear system (express all solutions as linear combinations of some vectors). Determine all solutions of the original non-homogeneous system in the form xp + xh.

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