Mathematics for Computer Scientists 2 (COMP1045 UNMC) (SPM1 24-25)
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If a set of vectors S is linearly independent in 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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The kernel of a linear mapping T: V -> W is always a subspace of:
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If W1 ∩ W2 = {0}, then Grassmann's Formula simplifies to:
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In R^2, the sum of two distinct lines passing through the origin is:
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Which axiom of a vector space states that for any scalar c in scalar field K and any vector u in E, the scalar multiple cu is also in E?
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If W1 and W2 are subspaces of V such that W1 ∩ W2 = {0}, then their sum W1 + W2 is a:
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Which of the following equations represents the distributivity of scalar multiplication over scalar addition axiom for scalars a and b in scaler field K and a vector u in a vector space V?
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If B1 is a basis for W1 and B2 is a basis for W2, and V = W1 ⊕ W2, then B1 ∪ B2 is a:
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The linear span of the empty set in a vector space V is:
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Linear Mapping I - Matrix Representation:
If T: R^n -> R^m is a linear mapping, then there exists a unique m x n matrix A such that for all x in R^n:
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