Question: Let X be a n-dimensional vector space over a field F, and let B = x 1 , ..., x n be an ordered basis

Let X be a n-dimensional vector space over a field F, and let B = x₁, ..., x_n be an ordered basis of X and S: X->X be a linear operator. If the matrix [S]_B is upper triangular, then prove Sxispan(x₁, ..., x_i) for i = 1, ..., n

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