I have a matrix;

$$X = \begin{bmatrix} x_{1,1} & x_{1,2} & ... & x_{1,k} \\ x_{2,1} & x_{2,2} & ... & x_{2,k} \\ \vdots & \vdots & \ddots & \vdots \\ x_{n,1} & x_{n,2} & ... & x_{n,k} \\\end{bmatrix}$$

And I want to zero out the elemenst $x_{1,1}$ and $x_{2,1}$. I have found lots of literature saying this can be done with Householder matrices but cannot seem to find any examples of to do it for elements in this way.

How can I do this using Householder matrices? Do I need knowledge of all the other elements of this matrix to do this or is this done just using the values of $x_{1,1}$ and $x_{2,1}$.


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