Kunze Linear Algebra · Problem 3.5.10

Linear Transformations

Mathematics — Methods · dimension-annihilated-subspace

Problem

Let FF be a subfield of the complex numbers. We define nn linear functionals on FnF^n (n≥2n \geq 2) by fk(x1,…,xn)=∑j=1n(k−j)xj,1≤k≤n.f_k(x_1, \ldots, x_n) = \sum_{j=1}^{n} (k - j) x_j, \quad 1 \leq k \leq n. What is the dimension of the subspace annihilated by f1,…,fnf_1, \ldots, f_n?

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