Hey guys!(adsbygoogle = window.adsbygoogle || []).push({});

I am having a major brain problem today, with this problem.

L is a linear transform that maps L:P_{4}[tex]\rightarrow[/tex]P_{4}

As such that (a_{1}t^{3}+a_{2}t^{2}+a_{3}t+a_{4}= (a_{1}-a_{2})t^{3}+(a_{3}-a_{4})t.

I am trying to find the basis for the kernel and range.

I know that the standard basis for P_{4}is {1,x,x^{2},x^{3}}

And the kernel is when L(u)=0, but I don't know how to find the transformation matrix, since we're not dealing with numbers in R, but in the set of polynomials. Is there another way to find the kernel/range and bases without using the T matrix?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Basis for kernel of linear transform

Loading...

Similar Threads - Basis kernel linear | Date |
---|---|

Procedure for orking out the basis of the kernel of a linear transformation. | Apr 19, 2012 |

What is the need for a separate basis for the kernel ? Please have a look at my expln | Mar 24, 2012 |

Linear Transformations,Find basis of kernel and range | Nov 4, 2010 |

Kernel, Range, Basis (linear algebra) | Dec 13, 2009 |

Basis of the kernel | Apr 12, 2008 |

**Physics Forums - The Fusion of Science and Community**