How can I increase the line spacing in a matrix?

You could redefine \arraystretch. This can be made locally, within a group or environment. For example:

\begingroup
\renewcommand*{\arraystretch}{1.5}
% your pmatrix expression
\endgroup

But you could do it in the preamble too, then it would have effect on all matrices and arrays.

Here's a redefinition of an internal amsmath LaTeX macro for customizing line spacing in specific matrices arbitrarily as desired:

\makeatletter
\renewcommand*\env@matrix[1][\arraystretch]{%
  \edef\arraystretch{#1}%
  \hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{*\c@MaxMatrixCols c}}
\makeatother

After putting this in your preamble, you can write

\begin{pmatrix}[1.5]
...

vary the value as you like, with pmatrix, vmatrix, bmatrix and alike, or use it without the optional argument as usually.

I used it similar in my blog some years ago.

Complete small example to show the difference:

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\renewcommand*\env@matrix[1][\arraystretch]{%
  \edef\arraystretch{#1}%
  \hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{*\c@MaxMatrixCols c}}
\makeatother
\begin{document}
\[
  \begin{pmatrix}
    1 & 0 \\
    0 & 1
  \end{pmatrix}
  =
  \begin{pmatrix}[1.5]
    1 & 0 \\
    0 & 1
  \end{pmatrix}
\]
\end{document}

By redefining \arraystretch you can change the vertical space between the all rows; using the optional argument for \\ you can control the vertical space for individual lines:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
\begin{pmatrix}
  \dfrac{a}{b} & c\\
  \dfrac{a}{b} & d\\
  \dfrac{a}{b} & e
\end{pmatrix}
\]

\[
\renewcommand\arraystretch{2}
\begin{pmatrix}
  \dfrac{a}{b} & c\\
  \dfrac{a}{b} & d\\
  \dfrac{a}{b} & e
\end{pmatrix}
\]

\[
\begin{pmatrix}
  \dfrac{a}{b} & c \\[1em]
  \dfrac{a}{b} & d\\[2em]
  \dfrac{a}{b} & e
\end{pmatrix}
\]

\end{document}