title: R inverting matrix with solve returning Error
body: <p>I am studying R programming.</p>
  
  <p>I am trying to inverting matrix. Below is what I have tried.  </p>
  
  <pre><code>x &lt;- matrix(1:16, 4, 4)
  x
  #      [,1] [,2] [,3] [,4]
  # [1,]    1    5    9   13
  # [2,]    2    6   10   14
  # [3,]    3    7   11   15
  # [4,]    4    8   12   16
  
  solve(x)
  # Error in solve.default(x) : 
  #  Lapack routine dgesv: system is exactly singular: U[3,3] = 0
  
  solve(x) %*% x
  # Error in solve.default(x) : 
  #  Lapack routine dgesv: system is exactly singular: U[3,3] = 0
  
  x %*% solve(x)
  # Error in solve.default(x) : 
  #  Lapack routine dgesv: system is exactly singular: U[3,3] = 0
  </code></pre>
  
  <p>I can not understand what 'singular' means. According to this <a href="http://www.inside-r.org/r-doc/base/solve" rel="nofollow">link</a>, it is said that if <code>solve</code> does not have second parameter, it inverts first parameter. </p>
  
  <p>I am fully confused, so need some explanation with example would be wonderful.</p>