Exercise 5.B.15

Answers

Proof. Suppose $V$ is finite-dimensional vector space. Let $v_{1}, \dots, v_{n}$ be a basis of $V$ . Define $T \in L (V)$ by

T v_{j} = v_{1} + \dots + v_{n}

$M (T)$ contains $1$ ’s in all its entries, but $T$ is clearly not invertible. □

celiopassos

2017-10-06 00:00