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10 Nov 2019
Problem shown in the image
Let V and W be finite dimensional vector s Let T V W and U W V be paces. linear and assume that dim(V) dim(W). rove that if U(T(r)) for all TE V then T (U(i)) y for all E W. Hint 1: Prove that nu 0 and use the given assumptions to conclude that T is onto. Hint 2: Since T is onto any i E W can be written as ij F T(2) for some 2 E V.
Problem shown in the image
Let V and W be finite dimensional vector s Let T V W and U W V be paces. linear and assume that dim(V) dim(W). rove that if U(T(r)) for all TE V then T (U(i)) y for all E W. Hint 1: Prove that nu 0 and use the given assumptions to conclude that T is onto. Hint 2: Since T is onto any i E W can be written as ij F T(2) for some 2 E V.
Sixta KovacekLv2
29 May 2019