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I've got two homogenous equations: 3x + 2y + z - u = 0 and 2x + y + z +5u = 0. I'm trying to find a basis for these solutions. The solution vectorx[x, y, z, u] is a solution if and only if it is orthogonal to the row vectors, in this caseaandb([3, 2, 1, -1], [2, 1, 1, 5)]. My understanding is that these row vectors span the space orthogonal tox, and they thus can be used as a basis. The answer given by the text I'm using gives for a basis these two vectors [1, -1, -1, 0] and [0, 6, -11, 1]. How were these basis vectors derived? I tried doing a linear combination ofaandbto get the textbook answer but I couldn't get that to work. Help!

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# Homework Help: Basis vectors and ortho solution spaces

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