Suppose that {v1, v2, . . . , vn} spans V and T∈L(V, W). Prove that {T(v1), T(v2), . . . , T(vn)} spans range(T).

Mathematics

1 answer:

serious [3.7K]3 years ago

3 0

Answer:

Step-by-step explanation:

it’s 6

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lina2011 [118]

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1 -3,45<br> Rational or irrational

Naddik [55]

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Step-by-step explanation:

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Define fn : [0,1] --> R by the

sasho [114]

Answer:

The sequence of functions $\{x^{n}\}_{n\in \mathbb{N}}$ converges to the function

$f(x)=\begin{cases}0&0\leq x$ .

Step-by-step explanation:

The limit $\lim_{n\to \infty }c^{n}$ exists and converges to zero whenever $\lvert c \rvert$ . But, if $c=1$ the sequence $\{c^{n}\}$ is constant and all its terms are equal to $1$ , then converges to $1$ . Using this result, consider the sequence of functions $\{f_{n}\}$ defined on the interval $[0,1]$ by $f_{n}(x)=x^{n}$ . Then, for all $0\leq x$ we have that $\lim_{n\to \infty}x^{n}=0$ . Now, if $x=1$ , then $\lim_{n\to \infty }x^{n}=1$ . Therefore, the limit function of the sequence of functions is