---
title: Assignments 2
tags: Linear algebra
GA: G-77TT93X4N1
---

# Assignments 2

1. Let ${\bf u}\ne {\bf v}$ be non-zero vectors in the vector space $V$. Prove that $\{\bf{u}, \bf{v}\}$ is linearly dependent if and only if $\bf{u}$ is a multiple of $\bf{v}$.
2. Let $T:P_3\to P_3$ be defined by $T(p(x))=xp'(x)$. Let $\beta=\{x^3, x^2, x, 1\}$ be the basis of $P_3$. Find $[T]_{\beta}$.
3. Consider $T:\mathbb{P}_2(R)\to \mathbb{P}_2(R)$, $T(p) = p'$, determine $\text{kernel}(T)$ and $\text{range}(T)$.
4. Exercise 5.5 at p.23.
5. Exercise 6.2 at p.29.

# TA solution

* [Assignment2_solution](https://drive.google.com/file/d/1BOqErDQ9sYdQTs5a1inmKGXLKlE1hsls/view?usp=sharing)