Question: 2. (5 points) Consider the linear, time-invariant system: i = Ar + Bu Here, r E R and u e Rm. We say a set

2. (5 points) Consider the linear, time-invariant system: i = Ar + Bu Here, r E R" and u e Rm. We say a set U is A-invariant if the following property holds: for any r e U, we have Are U. In other words, if we start with a c U, applying A will still keep us in U. Recall the definition of the controllability matrix: C = B AB ... An-1B] Prove that R(C) is A-invariant

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