Let X ∈ R3 be some xed vector with coordinates X1, X2, X3. Consider the action on vectors of the operator “cross-product by X”. In other words, it transforms vectors using the rule v → X × v. Since this is a linear operator, it is represented by some 3 × 3 matrix. Find this matrix in terms of X1, X2, X3. Is this matrix ever invertible?

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