## Linear Algebra: A Modern Introduction

$2$
For the matrices $u=\begin{bmatrix} u_{1} \\ u_{2} \\ \vdots\\ u_{n} \end{bmatrix}$ and $v=\begin{bmatrix} v_{1} \\ v_{2} \\ \vdots\\ v_{n} \end{bmatrix}$ The dot product is: $u\cdot v=u_1\cdot v_1+u_2\cdot v_2+...+u_n\cdot v_n.$ Hence: $u\cdot v=1\cdot 4+\sqrt2\cdot (-\sqrt2)+\sqrt3\cdot 0=4+(-2)+0=2.$