Mathematics for Computer Scientists 2 (COMP1045 UNMC) (SPM1 24-25)
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The associativity of scalar multiplication axiom states that for scalars a and b in scaler field K and a vector u in a vector space V:
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If W is a subspace of a finite-dimensional vector space V, then:
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Which of the following conditions must a transformation T: V -> W satisfy to be a linear mapping between vector spaces V and W?
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Steinitz' Lemma implies that all bases of a finite-dimensional vector space have the:
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A basis provides the most efficient way to represent vectors because the linear combination is:
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If a set of vectors S spans a finite-dimensional vector space V and the number of vectors in S is equal to the dimension of V, then S is:
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If W1 and W2 are subspaces of V such that dim(W1 + W2) = dim(W1) + dim(W2), then:
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If W1 and W2 are subspaces of a vector space V, then their intersection W1 ∩ W2 is
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Which of the following transformations T: R^2 -> R^2 is a linear mapping?
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The linear span of any subset S of a vector space V is always:
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