In Problems 114, a subset W of some n-space R n is defined by means of a
Question:
In Problems 1–14, a subset W of some n-space Rn is defined by means of a given condition imposed on the typical vector (x1 , x2 , ....,xn). Apply Theorem 1 to determine whether or not W is a subspace of Rn.
W is the set of all vectors in R3 such that x1 = 5x2.
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THEOREM 1 Conditions for a Subspace The nonempty subset W of the vector space V is a subspace of V if and only if it satisfies the following two conditions: (i) If u and v are vectors in W, then u + v is also in W. (ii) If u is in W and c is a scalar, then the vector cu is also in W.
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Suppose x x 1 x 2 x 3 and y y 1 y 2 y 3 are vectors in W so x 1 5x 2 and y 1 5y 2 Then thei...View the full answer
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Related Book For
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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