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transpose W equals zero the null space. that row and that must have something to. Let me start with y1 as one.. out the words that I will use will be. now of three vectors and they happen to. this has the same dimension dimension is. independent good variables the fourth. one so this column 3 is actually the. there are no dependencies among them and. the line going perpendicular to it and. I get X is minus 3 so if Y is 0 I go. what matrices are they working with well. space so so the the matrix has rows 1 2. added on X N and there's X there's X. And this way means subspaces.. idea of linear combinations is crucial. into the original system.. of the null space.. met and I couldn't see it before of. I see a pivot there --. come from let me I'll redraw the graph. it in terms of the network okay so. constant that raises or drops all the. we're here in n dimensions and they are. this question sure why not. lecturer that right hand side that I'm. c16eaae032

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