Question: (1)Let O denote the zero map O : R^n R^n, and let T : R^n R^n. Show that if T^k = O for some k,

(1)Let O denote the zero map O : R^n R^n, and let T : R^n R^n. Show that if T^k = O for some k, then T^n = O.

(2)Suppose T : R^n R^k , U : R^k R^m are linear maps. Show that nullity(U T) nullity(U) + nullity(T).

(1)Let O denote the zero map O : R^n R^n, and

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