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Let \(V\) be a vector space over \(\mathbb{R}\). A norm on \(V\) is a function \(\|\cdot \| : V \to \mathbb{R}\) satisfying the following properties:

Let \(V\) be a vector space over any field \(F\).

A collection of vectors \(v_1, v_2, \ldots, v_n \in V\) is called dependent if there exist real numbers ...

Consider the \(10\)-by-\(10\) matrix \(M\) for which the entry in the \(i^\text{th}\) row and \(j^\text{th}\) column is \(i+j\). What is the rank of ...

Compute the limit: \[\large\lim_{m\to\infty} \dfrac{1}{\ln(m)} \sum_{n=2}^{m} \dfrac{1}{n^{1 + \frac{1}{\ln(n)}}}.\]

Consider the \(2\)-by-\(2\) matrix \[A = \begin{pmatrix} 5 & 1 \\ -1 & 3 \end{pmatrix}. \] What is the trace of \(A^{100}?\)

\(\) Note: The trace of a ...

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