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4.4 Spanning Sets - Purdue University
Reducing the augmented matrix of this system to row-echelon form, we obtain 1 −24 x1 01−1 −x1 −x2 0007x1 +11x2 +x3 . It follows that the system is consistent if and only if x1, x2, x3 satisfy 7x1 +11x2 +x3 = 0. (4.4.4) Consequently, Equation (4.4.3) holds only for those vectors v = (x1,x2,x3) in R3 whose components satisfy Equation (4.4.4).
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