---
title: Assignments 4
tags: Linear algebra
GA: G-77TT93X4N1
---

# Assignments 4

1. Find the best approximation of $f(x)=e^x$ by a quadratic polynomial, with respect to the inner product
$$
\langle f, g\rangle = \int^1_{-1} f(x)g(x)\,dx.
$$
2. Exercise 1.9 at p.125.
3. Exercise 2.1 at p.128.
4. Exercise 3.10 at p.134.
5. (Prove it if the statement is true or give a counter example otherwise)
Let $L:V\to W$ be an isomorphism, $V$ and $W$ are inner product space. Suppose $\{v_1, \cdots, v_n\}$ is an orthogonal basis of $V$, then $\{L(v_1), \cdots, L(v_n)\}$ is also an orthogonal basis of $W$.

* [Assignment4_solution](https://drive.google.com/file/d/16ja11KPykS1aSN8Rqkw9G06OsZKETOkZ/view?usp=sharing)