title: How to calculate ker(A) / null space in R
body: <p>Within some matrix algebra I found the expression <code>B = ker(A)</code>, where A is a 3x4 transformation matrix. The following two links gave me some vague idea about ker() in general:</p>
  
  <p><a href="http://mathworld.wolfram.com/Kernel.html" rel="nofollow noreferrer">Wolfram: Kernel</a></p>
  
  <p><a href="https://math.stackexchange.com/questions/2109003/calculate-the-dimensions-and-basis-of-the-kernel-textkerf">Calculate the dimensions and basis of the kernel Ker(f)</a></p>
  
  <p>But frankly, I still can not square how to get a 4x1 vector as result. <strong>How would this kernel be calculated in R?</strong> And some additional background/links would be appreciated.</p>
  
  <p>Here is the matrix A and the result B (or its transpose...).</p>
  
  <pre><code>A = structure(c(0.9, 1.1, 1.2, 0.8, 0, 0.5, 0.3, 0.1, 0.5, 0, 0.2, 
  0.7), .Dim = 4:3)
  
  B = structure(c(0.533, 0.452, -0.692, -0.183), .Dim = c(4L, 1L))
  </code></pre>
  
  <p>I did get as far as realizing, that each row of the A-matrix times B equals zero, just like in the examples. But for solving the set of linear equations I am missing one more equation, don't I?</p>