Question $1$

Design the following three algorithms using the pseudocode presented in the class

Algorithm $1$: Implement the Householder transformation algorithm as a function householder$()$

that applies the householder transformation to $mn$ matrix $A.$

Employ the householder algorithm to obtain the orthogonal transformation of the following

matrix

$\left[\begin{array}{ccc}1& -1& 4\\ 1& 4& -2\\ 1& 4& 2\\ 1& -1& 0\end{array}\right]$

Note:

The function must work for a general $mn$ matrix where $m>n$

You cannot use a built$-$in Householder functions of the program.

The program should print the transformation that happens with matrix A after the

transformation of each column.

To pass this assessment, you must:

Include the complete code for the algorithm.

The functioning of the algorithm is illustrated by applying it to he above problem.

Obtain the correct final matrix after the transformation.