(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a kernel and image basis of the linear transformation having:

[tex] \displaystyle T:{{\mathbb{R}}^{3}}\to {{\mathbb{R}}^{3}}[/tex] so that

[tex] \displaystyle _{B}{{\left( T \right)}_{B}}=\left( \begin{matrix}

1 & 2 & 1 \\

2 & 4 & 2 \\

0 & 0 & 0 \\

\end{matrix} \right)[/tex]

[tex] \displaystyle B=\left\{ \left( 1,1,0 \right),\left( 0,2,0 \right),\left( 2,0,-1 \right) \right\}[/tex]

2. Relevant equations

3. The attempt at a solution

For the image basis it is easy given the fact that the rank of the associated matrix is 1 so, the image is generated by one column.

The problem comes when finding the Kernel basis. My idea is to save the general fromula of the linear map which would work for sure but I wanted to know if there's a quicker way of doing it without finding the general formula of the linear map.

Thanks!

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# Homework Help: Find a kernel and image basis of a linear transformation

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