Suppose V and W are finite-dimensional vector spaces, T E L(V, W) is invertible, and let...

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Suppose V and W are finite-dimensional vector spaces, T E L(V, W) is invertible, and let S E L(V, W). 2a) Show that null (T+ S) C range (T-¹S). 2b) Deduce from part a) that dim null (T+S) ≤ dim range S. Suppose V and W are finite-dimensional vector spaces, T E L(V, W) is invertible, and let S E L(V, W). 2a) Show that null (T+ S) C range (T-¹S). 2b) Deduce from part a) that dim null (T+S) ≤ dim range S.

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2a Let x null T S So T Sx 0 Hence Tx Sx 0 So Sx Tx ... View the full answer