Mathematics for Computer Scientists 2 (COMP1045 UNMC) (SPM1 24-25)
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A basis of a vector space V is a set of vectors that is:
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The commutativity of addition axiom for a vector space V states that for all vectors u and v in V:
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The image (or range) of a linear mapping T: V -> W, denoted Im(T), is defined as:
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The dimension of the zero subspace {0} is:
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If the kernel of a linear mapping T: V -> W contains a non-zero vector, then the set of vectors in V that map to that same vector in W is:
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A set of n vectors {v1, v2, ..., vn} in an n-dimensional vector space V is linearly independent if and only if the matrix formed by these vectors has a:
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A basis can be seen as a minimal:
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Which of the following linear mappings is an endomorphism?
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In Direct Sum, if W1 and W2 are subspaces of V, and every vector v ∈ (W1 + W2, +, .) can be uniquely written as v = w1 + w2 where w1 ∈ W1 and w2 ∈ W2, then
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Which of the following sets of vectors in R^3 is linearly dependent due to one vector being a scalar multiple of another?
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