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Mathematics for Computer Scientists 2 (COMP1045 UNMC) (SPM1 24-25)

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If B is a basis for a vector space V, then every vector in V can be written as:
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The image of the linear mapping T: R^2 -> R defined by T(x, y) = x - y is:
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Which of the following describes the closure under scalar multiplication axiom for a vector space V (where a is a scalar in scaler field K and u is a vector in V)?
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The kernel (or null space) of a linear mapping T: V -> W, denoted Ker(T), is defined as:
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If dim(V) = 5, dim(W1) = 3, dim(W1 ∩ W2) = 0, and dim(W1 + W2) = 5, then the minimum possible value for dim(W2) is:
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For a linear mapping T: V -> W, the domain of the mapping (i.e., dom (T)) is:
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The dimension of a finite-dimensional vector space V is defined as:
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Which axiom of a vector space states that for any two vectors u and v in E, their sum u + v is also in E?
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A set of vectors {v1, ..., vk} is linearly dependent if and only if there exist scalars c1, ..., ck, not all zero, such that:
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The linear span of a set of vectors S = {v1, v2, ..., vk} in a vector space V, denoted span(S), is:
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